Quantum Symmetric Pairs, Hecke Algebras, and Representations: Exploring Spherical Functions (Q-SPHERE 2026)

8 Jun 2026, 09:15 → 12 Jun 2026, 15:10 Europe/Amsterdam

Radboud University

Koelink, Maarten vanPruijssen (IMAPP, Radboud Universiteit), Philip Schlösser (Radboud University), Stein Meereboer

Q-SPHERE is a focused workshop bringing together researchers working at the intersection of representation theory, symmetric pairs, quantum symmetric pairs, and Hecke algebras. A central theme is the rich theory of spherical functions, both classical and quantum, and their deep connections with special functions, orthogonal polynomials, and their vector- and matrix-valued generalizations with applications in mathematical physics.

The workshop aims to highlight recent advances, foster new collaborations, and provide a platform for exchanging ideas across these interconnected areas. By exploring symmetry, from Lie theory to quantum groups, participants will engage with the algebraic and analytic structures that drive current developments in harmonic analysis and special functions.

Participation is free of charge, but registration is mandatory. The registration deadline is April 1, 2026.

We welcome experts, early-career researchers, and anyone interested in the vibrant interface of algebra, analysis, geometry and physics shaped by symmetry.

Confirmed Speakers:

• Andrea Appel (U. Parma)
• Kenny De Commer (VUB, Brussels)
• Yvann Gaudillot-Estrada (U. Lorraine)
• Jort de Groot (U. Amsterdam)
• Robin van Haastrecht (U. Gothenburg)
• Max van Horssen (U. Leuven)
• Mikhail Isachenkov (U. Amsterdam)
• Toshiyuki Kobayashi (U. Tokyo)
• Stefan Kolb (U. Newcastle)
• Tom Koornwinder (U. Amsterdam)
• Quentin Labriet (U. Montreal)
• Jules Lamers (U. Glasgow)
• Lucas Langen (U. Paderborn)
• Xinyang Liu (U. Newcastle)
• Marcelo de Martino (Forward College, Lisbon)
• Davide Dal Mertello (U. Padua)
• Marta Mazzocco (Polytechnical U. of Catalonia, Barcelona)
• Stein Meereboer (Radboud U., Nijmegen)
• Eric Opdam (U. Amsterdam)
• Michael Pevzner (U. Tokyo and U. Reims Champagne-Ardenne)
• Margit Rösler (U. Paderborn)
• Nobukazu Shimeno (Kwansei Gakuin U.)
• Philip Schlösser (Radboud U., Nijmegen)
• Jinfeng Song (Hong Kong U. of Science and Technology)
• Paul Terwilliger (U. of Wisconsin-Madison)
• Jasper Stokman (U. Amsterdam)
• Bart Vlaar (BIMSA, Beijing)
• Liao Wang (U. Bonn)
• Hideya Watanabe (Rikkyo U., Tokyo)
• Bob Yunken (U. Lorraine)

 

Organizers:

• Erik Koelink
• Stein Meereboer
• Maarten van Pruijssen
• Philip Schlösser

Warning

There are spam emails in circulation that enquire personal details in order to reserve/book hotel rooms for this conference. Do not respond to them or give them personal details. We will only ever contact you about this conference from email addresses ending in @ru.nl or @math.ru.nl.

Lecture rooms

The talks will be held in the following rooms:

• Mon--Wed: HG00.071
• Thu--Fri: HG00.307

Discussion room

For the duration of the workshop there will be room reserved for discussion and collaboration:

08/06/2026 09:00 - 08/06/2026 17:00 ; HG00.308
09/06/2026 09:00 - 09/06/2026 17:00 ; HG00.308
10/06/2026 09:00 - 10/06/2026 17:00 ; HG00.308
11/06/2026 09:00 - 11/06/2026 17:00 ; HG03.085
12/06/2026 09:00 - 12/06/2026 17:00 ; HG00.308

Getting around

The conference will take place at the Huygens building in the north-east of the

Radboud campus. For more detailed information please refer to https://www.ru.nl/en/services/getting-to-the-campus-and-parking/directions-and-accessibility.

 

The Radboud university is easily accessible via train, which is well connected to most European cities. At the train station of Nijmegen you can either take the bus or train to the university campus. You can check in to both train and bus with use of a bank, or credit card. For the speakers and participants situated at Guesthouse Vertoef finding your way to the university campus is easiest done by walking to the train station and continuing your journey from there, or by renting a bike for the week, e.g. ov-fiets.

Conference diner

The conference diner will take place at Arsenaal: Arsenaalpoort 1, 6511 PN Nijmegen, Nederland. 

book_of_abstracts.pdf

timetable.pdf

Monday 8 June

10:00 Registration

1 Stokman: Quasi-polynomial analogs of Askey-Wilson polynomials

I will first introduce quasi-polynomial analogs of the nonsymmetric and symmetric Askey-Wilson polynomials using an explicit representation of a rank one double affine Hecke algebra. In the second part of the talk, I will explain how they are related to Mizhan-Rahman's associated Askey-Wilson polynomials. The second part of the talk is joint work with Mikhail Isachenkov.

2 De Groot: An indefinite spectral triple for SU(1,1)

Spectral triples provide a noncommutative analogue of spin manifolds and play a central role in noncommutative geometry. While the compact Riemannian case is well understood, far less is known in the noncompact pseudo-Riemannian setting. In this talk, I will present the construction of an indefinite spectral triple for the Lie group SU(1,1), highlighting the role of representation theory in the construction. Moreover, I will explain how this example acts as a stepping stone towards a spectral triple for the quantum group SUq(1,1). This talk is based on arXiv:2601.22171.

12:15 Lunch

3 Vlaar: On quantum affine symmetric pairs (part 1)

The Yang–Baxter equation and the reflection equation, or boundary Yang–Baxter equation, are fundamental identities in quantum integrable systems, governing factorizable particle interactions on a line and on a half-line, respectively. While the Yang–Baxter equation is deeply connected to quantum groups, solutions of the reflection equation, called K-matrices, arise naturally from quantum symmetric pairs. In this two-part talk, we will survey recent joint work and open problems on quantum symmetric pairs, with special emphasis on affine type.

4 Appel: On quantum affine symmetric pairs (part 2)

The Yang–Baxter equation and the reflection equation, or boundary Yang–Baxter equation, are fundamental identities in quantum integrable systems, governing factorizable particle interactions on a line and on a half-line, respectively. While the Yang–Baxter equation is deeply connected to quantum groups, solutions of the reflection equation, called K-matrices, arise naturally from quantum symmetric pairs. In this two-part talk, we will survey recent joint work and open problems on quantum symmetric pairs, with special emphasis on affine type.

15:40 Coffee and tea break

5 Lamers: The spin-Ruijsenaars-Macdonald system

In this talk I will revisit the spin-Ruijsenaars–Macdonald system, given by a matrix-valued generalisation of Macdonald operators that arises in the context of induced modules of double affine Hecke algebra and fits in a quantum-affine version of Schur–Weyl duality. After reviewing the construction of this system, I will outline recent developments, including elliptic generalisations and applications to quantum spin chains with long-range interactions.

17:00 Drinks & Bites organized by W.S.V. DESDA

Tuesday 9 June

6 Kolb: Short star products for quantum symmetric pairs

Short star products are filtered deformations of graded algebras satisfying a truncation condition first considered by Beem-Peelaers-Rastelli and further developed by Etingof and Stryker. In this talk I will explain that quantum symmetric pair coideal subalgebras are realized as short star products on quantum horospherical subalgebras. The shortness property allows for immediate conceptual interpretations of antiautomorphisms and bar-involutions which had previously been constructed via the quasi K-matrix. Moreover, this perspective allows us to express the quasi K-matrix in terms of the quasi R-matrix of Drinfeld and Lusztig. The talk is based on joint work with Milen Yakimov.

7 Wang: Weight modules for gl_2 \times \gl_2

We develop a theory of weights for the quantum symmetric pair $(\mathfrak{gl}_4,\mathfrak{gl}_2\times\mathfrak{gl}_2)$ of type AIII. We define ``magical'' operators that are compatible with weight spaces (wrt. Letzter's Cartan subalgebra) and use them to study Verma modules and irreducible quotients. We then prove the existence of weight bases in tensor products by explicitly constructing some highest weight vectors. These constructions allow us to mimic the important aspects of the classical finite dimensional representation theory.
Applications include a definition of rational representations, the BGG resolution, a Clebsch--Gordan formula, the Harish-Chandra isomorphism and central characters, as well as a classification and description of all irreducible polynomial representations.

8 Meereboer: Kostant's branching law for quantum symmetric pairs

Kostant's branching law for a symmetric pair $(\mathfrak{g},\mathfrak{k})$ determines the multiplicity of a irreducible $\mathfrak{k}$-module inside irreducible $\mathfrak{g}$-modules. In this talk I will explain how to derive this branching law using the language of Watanabe's integrable modules for quantum symmetric pairs. This is joint work in progress with Stefan Kolb.

10:40 Coffee and tea break

9 Watanabe: Quantizations of coordinate algebras of symmetric pair subalgebras

It is known that the quantum coordinate algebra of a Kac--Moody algebra and its crystal basis admit Peter--Weyl type decompositions.
Also, Kashiwara proved that, for finite type, the crystal basis is isomorphic to the crystal basis of the modified quantum group as bicrystals.
The main topic of this talk is quantum symmetric pair analogues of these results.
In particular, I will show you some examples of "bi-icrystals" of type A.
This talk is partly based on a joint work with Mao Hoshino.

12:10 Lunch

10 Song: Representations of quantum symmetric pairs at roots of 1

The celebrated work of De Concini–Kac–Procesi established that the representation theory of quantum groups at roots of unity is closely linked to the conjugacy classes of the underlying group. In this talk, we extend this approach to quantum symmetric pairs.

For an i-quantum group $U^\imath$ associated with an involution θ, we consider a De Concini–Kac type integral form and study its specialization $U^\imath_ε$ at an odd root of unity. We show that the simple modules of $U^\imath_ε$ are parametrized by θ-twisted conjugacy classes of the underlying group and provide an explicit upper bound on their dimensions. Moreover, this bound is attained for simple modules corresponding to generic twisted conjugacy classes. Along the way, we construct a finite-dimensional coideal subalgebra of the Lusztig small quantum group.

This is joint work with Weinan Zhang.

11 Liu: Representation Theory of very non-standard quantum so(2N)

We study finite-dimensional representations of the quantum group analogue of $\mathfrak{so}_{2N}$ inside $\mathfrak{so}_{2N+1}$ appearing in the theory of quantum symmetric pairs. Using a Verma module approach, we classify finite-dimensional simple modules in terms of highest weights. These highest weights are joint eigenvalues of the Letzter-Cartan subalgebra. Using a modified $\mathfrak{sl}_2\times\mathfrak{sl}_2$-argument, we explicitly determine the highest weights of finite-dimensional irreducible representations.

12 Schlösser: Inner Product Methods for Matrix Spherical Functions

Given a quantum symmetric pair $(U,B)$, it is a well-known fact that (with some caveats) the (elementary) zonal spherical functions (ZSF) restrict to symmetric Macdonald polynomials.
We use the Haar functional on $U$'s dual to construct an inner product for the matrix spherical functions (MSF). Since the MSF form a free module over the ZSF, we can interpret this inner product to be related to an inner product with a matrix weight that is closely related to the Macdonald weight.

This inner product can be used to identify MSF with intermediate Macdonald polynomials in several example cases.

This talk is based on the preprint 2511.23367, which is joint work with Stein Meereboer.

15:40 Coffee and tea break

13 Isachenkov: Spin graph functions for the Lorentz group

Spin graph functions of Reshetikhin-Stokman are generalizations of vector-valued spherical functions that arise in many contexts in harmonic analysis and physics. In this talk I will consider a special class of spin graph functions for the (identity connected component of the) Lorentz group SO$(n,1)_e$, which is relevant for the analysis of Euclidean four-point local correlation functions in $(n-1)$-dimensional conformal field theory. I will present a construction, mapping such smooth spin graph functions to smooth vector-valued functions on a certain Cartan subgroup of the Lorentz group, and discuss the pushforward under that map of the algebra of invariant differential operators acting on the spin graph functions. This in particular provides an explicit representation of the corresponding algebra of quantum Hamiltonians by endomorphism-valued differential operators. The talk is based on the joint work with Edward Berengoltz and Jasper Stokman.

Wednesday 10 June

14 Terwilliger: The q-Onsager algebra and its finite-dimensional irreducible modules

This talk is about the $q$-Onsager algebra $O_q$. The algebra $O_q$ is defined by two generators and two relations called the $q$-Dolan/Grady relations. We will describe the finite-dimensional irreducible $O_q$-modules $V$ that satisfy a mild assumption. We will show that the $O_q$-generators act on $V$ as a tridiagonal pair. We will describe the tridiagonal pairs and the related tridiagonal systems, using the concept of a tetrahedron diagram. We will classify up to isomorphism the tridiagonal systems, and explain which ones come from an $O_q$-module.

15 van Haastrecht: Principal series induced from Heisenberg parabolic subgroups

Let $G$ be a semisimple Lie group and $K$ the maximal compact subgroup. Principal series representations of $G$ induced from a parabolic subgroup $P = MAN$ whose unipotent radical $N$ is abelian have been well studied. The analysis of these representations exploits the fact that $(K,L)$ has the structure a symmetric pair, where $L = K \cap M$. The next easiest case is when $N$ has the structure of a Heisenberg group. We study principal series representations induced from Heisenberg parabolic subgroups and we use the Peter-Weyl theorem for circle bundles over a symmetric space of $K$ to analyze these representations. We study reducibility, complementary series, and unitary subrepresentations, with a focus on $SL(n+2,\mathbb{R})$ and $G_{2(2)}$. This talk is based on joint work with Jan Frahm, Clemens Weiske and Genkai Zhang.

16 Langen: Uniform bounds on the Dunkl kernel

In Dunkl theory the Dunkl kernel replaces the classical exponential function in its predominant role in harmonic analysis. For regular spectral parameters, we present upper bounds for the Dunkl kernel and its derivatives which are uniform in the spatial variable. These estimates generalize sharp uniform upper bounds for spherical functions of Cartan motion groups and classical Bessel functions. The proof is based on an asymptotic study of the differential system satisfied by the Dunkl kernel with respect to parabolic subgroups of the Weyl group. As a consequence we obtain results regarding the Lebesgue density of the representing measure of Dunkl’s intertwining operator.

10:40 Coffee and tea break

17 Dal Martello: A crystallographic take on (rank n) GDAHA

Aiming for a revival of the dormant theory of crystallographic complex reflection groups, we give Coxeter-like reflection presentations for the top family of such groups. These new presentations behave à la Coxeter—encoding many of the group's properties at a glance—and further achieve the braid theorem, allowing to deform into the generic Hecke algebra. As part of a final showcase of the theory's promising future, the whole GDAHA family is rethought of as an elementary example in this new lingo.

12:10 Lunch

18 Mazzocco: Quantum middle convolution on rank 1 DAHA

The Riemann--Liouville fractional integral interpolates iterated integration to non-integer orders and turns a hypergeometric solution of rank $p$ into one of rank $p+1$. Katz recast this into the so-called \emph{middle convolution}, an operation on local systems on the punctured Riemann sphere that preserves the rigidity index. Dettweiler and Reiter subsequently made the operation explicit at the matrix level, as an action either on the residues of a Fuchsian system (additive middle convolution) or on the monodromy representation (multiplicative middle convolution). In this talk I will first recall the Riemann--Liouville transform and both the additive and the multiplicative middle convolutions of Dettweiler--Reiter, and then describe a noncommutative analogue of the multiplicative case --- a \emph{quantum middle convolution} --- built by enlarging the standard Hecke triple of the rank-one DAHA of type $\check{C}_1 C_1$ to a cyclic Noumi--Stokman-type quadruple and performing an explicit two-step quotient by the resulting invariant subspaces. Applied to the basic representation, this construction yields an explicit intertwiner between the basic representations with parameters $(a,b,c,d)$ and $(c,b,a,d)$. On the spherical subalgebra this operation reduces to the identity, recovering the $W(D_4)$ action on the Askey--Wilson / Zhedanov algebra; on the full DAHA basic representation it provides a new and explicit incarnation of the parameter symmetry $a \leftrightarrow c$.

19 Koornwinder: Local extension and automorphisms of rank 1 DAHA and related special functions

Consider the rank 1 DAHA of type $\check C_1 C_1$ with generators $T_1$, $T_0$, $Z$, $Z^{-1}$ and depending on the Askey--Wilson parameters $a,b,c,d,q$. Its basic representation is a faithful representation on the space of Laurent polynomials in $z$. We extend the generators $Z,Z^{-1}$ to all rational functions in $Z$. Then the basic representation extends to a faithful representation on the space of rational functions in $z$. Then the mapping sending a rational function $f(z)$ to $f(z^{-1})$ can be lifted to the extended DAHA, and similarly for the mapping sending $f(z)$ to $f(qz)$.

A DAHA automorphism is a parameter transformation $(a,b,c,d)\to(a'.b',c',d')$ together with an algebra isomorphism, depending on $a,b,c,d$, from the (extended) DAHA $H_{a,b,c,d}$ to $H_{a',b',c',d'}$. For each parameter transformation we define explicit isomorphisms $H_{a,b,c,d}\to H_{a',b',c',d'}$ which we call canonical. This can be done in particular for the $a \leftrightarrow c$ flip discussed in Mazzocco's lecture. More general isomorphisms $H_{a,b,c,d}\to H_{a',b',c',d'}$ factorize as a canonical isomorphism followed by a DAHA automorphism $H_{a',b',c',d'}\to H_{a',b',c',d'}$, which turns out to be a conjugation in many examples.

Many special DAHA automorphisms can be easily read off from the relations for the DAHA generators, but they are usually not canonical. We discuss some examples, and also their factorization. Some examples imply transformation formulas of non-symmetric Askey--Wilson polynomials (or functions), which functions occur as eigenfunctions of $Y=T_1 T_0$ in the basic representation.

15:40 Coffee and tea break

20 De Martino: A Quantized Metaplectic Howe Duality in Rank One

Dirac-type operators and Howe dualities provide a uniform approach to decomposition problems and symmetry algebras in the orthogonal and symplectic settings. Quantizing these structures is subtle and in the orthogonal Dirac setting competing frameworks do not currently agree.

In this talk I focus on the symplectic (metaplectic) Howe duality in the first nontrivial case, rank one, and present an explicit and computable quantization, based on joint work with M. Brito. The main outcome is a clean quantum duality in which both sides are Drinfeld–Jimbo sl(2)-type quantum groups (with different deformation parameters), realized via Hayashi’s deformed Weyl algebra. I will outline the resulting quantum analogues of the classical realization, Fischer-type structure, monogenics, and first-order symmetries, and conclude with the main obstacles to extending the construction beyond rank one.

18:00 Diner

Conference diner at Arsenaal.

Thursday 11 June

21 Kobayashi: Stability regions of branching multiplicities

In this talk, we discuss a conceptual perspective on when and how branching multiplicities change in restrictions of representations. We develop a framework for the stability of branching multiplicities arising in the restriction of finite- and infinite-dimensional representations of real reductive Lie groups.

Focusing on pairs whose complexifications are of type (gl(n+1), gl(n)) and (o(n+1),o(n)), we show that branching multiplicities are locally constant on explicitly described convex regions in the joint parameter space of infinitesimal characters, and can change only upon crossing certain hyperplanes (``fences'').

To illustrate the structure concretely, we describe these regions explicitly in the case of tensor products for sl(2), and in connection with this, Pevzner’s talk will discuss the parameter dependence of the blow-up of branching multiplicities in relation to the parameter dependence of Jacobi polynomials.

22 Pevzner: On blow-up phenomena for fusion rules

Controlling multiplicities in branching problems is a central question
in representation theory. In the setting of infinite-dimensional representations of real reductive Lie groups, analytic methods based on symmetry breaking operators provide one explanation of a surprising blow-up phenomena mentioned in the talk by T. Kobayashi.
We shall present this approach considering the basic case of $\mathfrak{sl}_2$ with a particular emphasis on the interplay with the classical theory of special functions.

10:40 Coffee and tea break

23 Shimeno: Matrix-valued spherical functions on semisimple Lie groups

Harish-Chandra's c-function on a real semisimple Lie group gives the leading coefficient of the zonal spherical function and determines the Plancherel measure for the spherical transform. Gindikin and Karpelevič gave an explicit formula for the c-function. Moreover, Heckman and Opdam developed a theory of hypergeometric functions associated with root systems, which are generalizations of zonal spherical functions.

In the case of spherical functions for non-trivial K-types, explicit formulae for c-functions and spherical inversions have been known for a few cases, including the case of one-dimensional K-types. In this talk, I will explain that for certain class of K-types, associated elementary spherical functions can be written by Opdam's non-symmetric hypergeometric functions. As corolaries, we have explicit formulae of c-functions and inversion formulae for the spherical transforms.

This talk is based on joint work with Hiroshi Oda.

12:10 Lunch

24 Rösler: Limits of Bessel functions for root systems as the rank tends to infinity

In this talk, we consider the asymptotic behaviour of Dunkl-type Bessel functions associated with root systems of type A and type B with positive multiplicities as the rank tends to infinity.
To obtain limits, one has to take sequences of spectral parameters which are of Vershik-Kerov type, i.e. tend to infinity in a suitable way. The situation is similar to the case of Heckman-Opdam polynomials whose limits were studied by Okounkov and Olshanski more than 20 years ago. Nowadays, there is renewed interest in such topics within the area of integrable probability.

We characterize both the possible limit functions as well as the spectral sequences for which limits of Bessel functions can be obtained, both in the cases of type A and type B.
For multiplicities related to group cases, these results have an interpretation in the context of asymptotic harmonic analysis in the sense of Olshanski.

The talk is based on joint work with Dominik Brennecken

25 van Horssen: Shift operators for non-symmetric Heckman-Opdam polynomials and non-symmetric Macdonald-Koornwinder polynomials

We present an algebraic construction of shift operators for the non-symmetric Heckman-Opdam polynomials and the non-symmetric Macdonald-Koornwinder polynomials. To each linear character of the finite Weyl group, we associate forward and backward shift operators, which are differential-reflection and difference-reflection operators that satisfy certain transmutation relations with the Dunkl-Cherednik operators. In the Heckman-Opdam case, the construction recovers the non-symmetric shift operators of Opdam and Toledano Laredo for the sign character.

This talk is based on joint work with Maarten van Pruijssen (arXiv:2602.06784).

26 Gaudillot-Estrada: A Mackey Analogy for real semisimple quantum groups

For a given real semisimple group $G$, the Mackey analogy consists of a collection of explicit relationships between the groups algebra of $G$ and that of its Cartan motion group $G_0$. The weakest of these relationships is the Connes-Kasparov isomorphism $K_*(C^*(G_0)) \cong K_*(C^*_r(G))$. In this talk, on the basis of small dimensional examples, I will explain why this analogy may also hold for real semisimple quantum groups, which have been introduced by De Commer.

15:40 Coffee and tea break

27 Labriet: Bivariate Jacobi polynomials via the rank 2 Jacobi algebra

Bivariate Jacobi polynomials is a family of orthogonal polynomials on the triangle that are solutions to a second order differential equation. This talk will present an algebraic interpretation for this family of polynomials based on the representation theory of the so-called rank 2 Jacobi algebra.

Friday 12 June

28 Yuncken: Crystallization of function algebras on semisimple groups.

The structure theory of the finite dimensional representations of a quantized enveloping algebra undergoes a massive simplification when the deformation parameter q goes to 0. This is the fundamental observation in the theory of crystal bases of Kashiwara and Lusztig. On might ask if there is a similar simplification of the Pontrjagin dual, meaning a crystallisation of the quantized algebra of functions on a compact semisimple Lie group. The answer is that the crystal limit is a combinatorial algebra associated to symbolic dynamics. I will describe this crystal limit, as well as its analogue for the noncompact group SL(2,C).
(Joint work with Marco Matassa and Aidan Sims.)

Speaker: Bob Yuncken

29 Opdam: Non symmetric shift operators

(Joint work with Valerio Toledano Laredo)

The well known "Dunkl operators" associated to a finite real reflection group constitute a commutative parameter family of deformations of the directional derivatives in Euclidean space. These operators are "differential-reflection" operators. Heckman and Cherednik have defined trigonometric versions of Dunkl's operators. The interest for these
operators lies in their deep ties to Macdonald polynomials and hypergeometric functions, to the Calogero-Moser quantum integrable system, and to the representation theory
of Hecke algebras.

"Hypergeometric shift operators" are tools to study Weyl group symmetric structures and functions in these contexts. In the present talk we present a theorem of existence and uniqueness of ''nonsymmetric shift operators'' for the Dunkl operators themselves. These nonsymmetric
shift operators are differential-reflection operators which "shift"
the parameters of the Dunkl operators by integers by means of a "transmutation relation".

10:40 Coffee and tea break

30 De Commer: A Kazhdan-Lusztig theorem in type B

Braided monoidal categories are governed by braid groups of type A and the associated Yang-Baxter equation. Given a semisimple compact Lie group G, the Kazhdan-Lusztig theorem gives a non-trivial equivalence between two particular braided monoidal unitary categories: one constructed from a non-trivial associator on the category of unitary G-representations, using solutions to the so-called KZ-equation, and one constructed as the representation category of the quantization of G. In this talk, we will explain how the Kazhdan-Lusztig theorem has an analogue `in type B’, with quantum groups replaced by coideals and braided monoidal categories replaced by braided module categories, which are governed by braid groups of type B and the associated reflection equation. This is based on joint work with S. Neshveyev, L. Tuset and M. Yamashita.

12:10 Lunch