Branching Rules for Finite-Dimensional Uq((3))$\mathcal {U}_{q}(\mathfrak {su}(3))$-Representations with Respect to a Right Coideal Subalgebra

ALDENHOVEN, NOUD; KOELINK, ERIK; ROMÁN, PABLO

Algebras and Representation Theory

SPRINGER

Año: 2017 vol. 20 p. 821 - 842

1386-923X

We consider the quantum symmetric pair (Formula presented.) where (Formula presented.) is a right coideal subalgebra. We prove that all finite-dimensional irreducible representations of (Formula presented.) are weight representations and are characterised by their highest weight and dimension. We show that the restriction of a finite-dimensional irreducible representation of (Formula presented.) to (Formula presented.) decomposes multiplicity free into irreducible representations of (Formula presented.). Furthermore we give explicit expressions for the highest weight vectors in this decomposition in terms of dual q-Krawtchouk polynomials.