Markov Processes on the Duals to Infinite-Dimensional Classical Lie Groups

Abstract

We construct a four parameter (z, z', a, b) family of Markov dynamics that preserve the z-measures on the boundary of the branching graph for classical Lie groups of type B, C, D. Our guiding principle is the "method of intertwiners" used previously in [7] to construct Markov processes that preserve the zw-measures.