Some examples of matrix-valued bispectral discrete orthogonal polynomials

We propose a method to construct matrix-valued orthogonal polynomials using the conjugation of a diagonal matrix weight by a matrix polynomial of degree 1. The method eventually yields bispectral sequences as eigenfunctions of second-order difference operators. This general framework extends the discrete families in the classical Askey scheme to the matrix setting by producing explicit matrix analogues of the Krawtchouk, Hahn, Meixner, and Charlier polynomials. Our results include explicit expressions for the weights, the orthogonal polynomials, and the corresponding difference operators.