paper

Little $q$ -Jacobi polynomials and symmetry breaking operators for $U_{q} (s l_{2})$

arXiv:2506.23848

Abstract

This paper presents explicit formulas for intertwining operators of the quantum group $U_{q} (s l_{2})$ acting on tensor products of Verma modules. We express a first set of intertwining operators (the holographic operators) in terms of the little $q$ -Jacobi polynomials, and we obtain for the dual set (the symmetry breaking operators) a $q$ -deformation of the Rankin--Cohen operators. The Verma modules are realised on polynomial spaces and, interestingly, we find along the way the need to work with non-commuting variables. Explicit connections are given with the Clebsch--Gordan coefficients of $U_{q} (s l_{2})$ expressed with the $q$ -Hahn polynomials.

20 pages

Little q-Jacobi polynomials and symmetry breaking operators for Uq​(sl2​)

Abstract

Little $q$ -Jacobi polynomials and symmetry breaking operators for $U_{q} (s l_{2})$