Branching Rules for Finite-Dimensional Uq(Su(3))-Representations with Respect to a Right Coideal Subalgebra

Abstract

We consider the quantum symmetric pair (Uq(Su(3)) , B) where B is a right coideal subalgebra. We prove that all finite-dimensional irreducible representations of 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 Uq(Su(3)) to B decomposes multiplicity free into irreducible representations of B. Furthermore we give explicit expressions for the highest weight vectors in this decomposition in terms of dual q-Krawtchouk polynomials.