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 d- spherical dual of the group U(n + 1), for a fixed finite dimensional irreducible representation d of U(n). The transition matrix comes from the three term recursion relation satisfied by a sequence of matrix valued orthogonal polynomials built up from the irreducible spherical functions of type d of SU(n + 1). One of the stochastic models is an urn model and the other is a Young diagram model.