Two stochastic models of a random walk in the U(n)-spherical duals of U(n+1)

Abstract

The random walk to be considered takes place in the - spherical dual of the group U(n + 1), for a xed nite dimensional irreducible representation of U(n). The transition matrix comes from the three term recursion relation satised by a sequence of matrix valued orthogonal polynomials built up from the irreducible spherical functions of type of SU(n + 1). One of the stochastic models is an urn model and the other is a Young diagram model.