Matrix-Valued Little q-Jacobi Polynomials

Matrix-valued analogues of the little q-Jacobi polynomials are introduced and studied. For the 2x2-matrix-valued little q-Jacobi polynomials explicit expressions for the orthogonality relations, Rodrigues formula, three-term recurrence relation and their relation to matrix-valued q-hypergeometric series and the scalar-valued little q-Jacobi polynomials are presented. The study is based on a matrix-valued q-difference operator, which is a q-analogue of Tirao's matrix-valued hypergeometric differential operator.Comment: 16 pages, various corrections and minor additions, incorporating referee's comment

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

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.Fil: Aldenhoven, Noud. Radboud Universiteit Nijmegen; Países BajosFil: Koelink, Erik. Radboud Universiteit Nijmegen; Países BajosFil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentin