Quantum symmetric spaces and related q-orthogonal polynomials

TL;DR

This paper introduces quantum analogues of classical symmetric spaces using reflection equations and explores their zonal spherical functions in relation to q-orthogonal polynomials.

Contribution

It presents a new class of quantum symmetric spaces and links their spherical functions to q-orthogonal polynomials, expanding the understanding of quantum harmonic analysis.

Findings

Defined quantum symmetric spaces via reflection equations

Connected zonal spherical functions to q-orthogonal polynomials

Provided foundational framework for quantum harmonic analysis

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.