Quantum symmetric spaces and related q-orthogonal polynomials

Abstract

A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal polynomials.

Cited by in corpus (29)

• Quantum symmetric Kac-Moody pairs
• Quantum group symmetry in sine-Gordon and affine Toda field theories on the half-line
• Coideal subalgebras in quantum affine algebras
• Self-dual Koornwinder-Macdonald polynomials
• Coideal Subalgebras and Quantum Symmetric Pairs
• Bethe Subalgebras in Twisted Yangians
• Universal K-matrices for quantum Kac-Moody algebras
• Integrable systems from the classical reflection equation
• Coideal algebras from twisted Manin triples
• $SO(N{)}_2$ Braid group representations are Gaussian
• Non-Levi closed conjugacy classes of SP_q(2n)
• Quantum geometry of algebra factorisations and coalgebra bundles
• Generalized q-Onsager Algebras and Dynamical K-matrices
• Quantum flag manifolds, quantum symmetric spaces and their associated universal K-matrices
• Quantum symmetric pairs and representations of double affine Hecke algebras of type $C^{\vee }{C}_n$
• Solutions of the $U_q({\widehat{\mathfrak{sl}}}_N)$ reflection equations
• Defining relations for quantum symmetric pair coideals of Kac-Moody type
• Dualities for spin representations
• Right coideal subalgebras in $U_q({\mathfrak{sl}}_{n+1}).$
• Canonical bases of a coideal subalgebra in $U_q({\mathfrak{sl}}_2)$
• On BC type basic hypergeometric orthogonal polynomials
• Twisted WZW Branes from Twisted REA's
• On representations of $U_q^{\prime }s{o}_n$
• A family of quantum projective spaces and related q-hypergeometric orthogonal polynomials
• Some remarks on the construction of quantum symmetric spaces
• Radial part calculations for quantum symmetric pairs with simple generators
• Stokes phenomenon and reflection equations
• Some limit transitions between BC type orthogonal polynomials interpreted on quantum complex Grassmannians
• Branching rules for finite-dimensional ${\mathcal{U}}_q(\mathfrak{su}(3))$-representations with respect to a right coideal subalgebra