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

TL;DR

This paper studies the restriction of finite-dimensional irreducible representations of the quantum group f(f(f(3)) to a right coideal subalgebra, showing multiplicity-free decompositions and explicit highest weight vectors involving dual q-Krawtchouk polynomials.

Contribution

It characterizes irreducible representations of the coideal subalgebra and provides explicit formulas for highest weight vectors in the decomposition.

Findings

Representations are weight representations characterized by highest weight and dimension.

Restriction decomposes multiplicity-free into irreducible representations.

Explicit highest weight vectors are expressed via dual q-Krawtchouk polynomials.

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.