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.

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 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.

Monday 8 June

10:00 → 11:00 Registration

11:00 → 11:50 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.

11:50 → 12:15 de Groot

12:15 → 14:00 Lunch

14:00 → 14:50 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.

14:50 → 15:40 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 → 16:10 Coffee and tea break

16:10 → 17:00 Lamers

17:00 → 18:00 Drinks & Bites

Tuesday 9 June

09:00 → 09:50 Kolb

09:50 → 10:15 Meereboer

10:15 → 10:40 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.

10:40 → 11:20 Coffee and tea break

11:20 → 12:10 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 → 14:00 Lunch

14:00 → 14:50 Song

14:50 → 15:15 Liu

15:15 → 15:40 Schloesser

15:40 → 16:10 Coffee and tea break

16:10 → 17:00 Isachenkov

Wednesday 10 June

09:00 → 09:50 De Martino

09:50 → 10:15 van Haastrecht

10:15 → 10:40 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 → 11:20 Coffee and tea break

11:20 → 12:10 Mazzocco

12:10 → 14:00 Lunch

14:00 → 14:50 Dal Martello

14:50 → 15:40 Koornwinder

15:40 → 16:10 Coffee and tea break

16:10 → 17:00 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.

18:00 → 20:00 Diner

Thursday 11 June

09:00 → 09:50 Pevzner

09:50 → 10:40 Kobayashi

10:40 → 11:20 Coffee and tea break

11:20 → 12:10 Shimeno

12:10 → 14:00 Lunch

14:00 → 14:50 Rösler

14:50 → 15:15 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).

15:15 → 15:40 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 → 16:10 Coffee and tea break

16:10 → 17:00 Labriet

Friday 12 June

09:00 → 09:50 Yuncken

09:50 → 10:40 Opdam

10:40 → 11:20 Coffee and tea break

11:20 → 12:10 de Commer

12:10 → 14:00 Lunch