Branching rules for finite-dimensional ${\mathcal{U}}_q(\mathfrak{su}(3))$-representations with respect to a right coideal subalgebra

Abstract

We consider the quantum symmetric pair $({\mathcal{U}}_q(\mathfrak{su}(3)),\mathcal{B})$ where $\mathcal{B}$ is a right coideal subalgebra. We prove that all finite-dimensional irreducible representations of $\mathcal{B}$ are weight representations and are characterised by their highest weight and dimension. We show that the restriction of a finite-dimensional irreducible representation of ${\mathcal{U}}_q(\mathfrak{su}(3))$ to $\mathcal{B}$ decomposes multiplicity free into irreducible representations of $\mathcal{B}$. Furthermore we give explicit expressions for the highest weight vectors in this decomposition in terms of dual $q$-Krawtchouk polynomials.

21 pages, 3 figures

References in corpus (1)

• Matrix Valued Orthogonal Polynomials for Gelfand Pairs of Rank One