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

Contribution List

3. Stokman: Quasi-polynomial analogs of Askey-Wilson polynomials

08/06/2026, 11:00

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.

10. Vlaar: On quantum affine symmetric pairs (part 1)

08/06/2026, 14:00

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...

11. Appel: On quantum affine symmetric pairs (part 2)

08/06/2026, 14:50

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...

7. Wang: Weight modules for gl_2 \times \gl_2

09/06/2026, 10:15

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...

5. Watanabe: Quantizations of coordinate algebras of symmetric pair subalgebras

09/06/2026, 11:20

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...

8. Langen: Uniform bounds on the Dunkl kernel

10/06/2026, 10:15

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...

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

10/06/2026, 16:10

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...

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

11/06/2026, 15:15

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...