Matrix-valued little qq-Jacobi polynomials

Matrix-valued analogues of the little qq-Jacobi polynomials are introduced and studied. For the 2×22×2-matrix-valued little qq-Jacobi polynomials explicit expressions for the orthogonality relations, Rodrigues formula, three-term recurrence relation and their relation to matrix-valued qq-hypergeometric series and the scalar-valued little qq-Jacobi polynomials are presented. The study is based on a matrix-valued qq-difference operator, which is a qq-analogue of Tirao’s matrix-valued hypergeometric differential operator.