Matrix-valued Classical Pairs Related to Compact Gelfand Pairs of Rank One: Families and Shift Operators

Abstract Given a matrix-valued classical pair related to a compact Gelfand pair of rank one, we provide an algorithm to introduce an extra parameter so that the corresponding families of matrix-valued orthogonal polynomials are related by a shift operator (differentiation). We provide a number of examples for which our algorithm is effective. In this way we find new examples and we recover existing examples that have been obtained with another method.