Two constructions of Markov chains on the dual of U(n)

Abstract

We provide two new constructions of Markov chains which had previously arisen from the representation theory of the infinite-dimensional unitary group. The first construction uses the combinatorial rule for the Littlewood-Richardson coefficients, which arise from tensor products of irreducible representations of the unitary group. The second arises from a quantum random walk on the group von Neumann algebra of U(n), which is then restricted to the center. Additionally, the restriction to a maximal torus can be expressed in terms of weight multiplicities, explaining the presence of tensor products.

17 pages

References in corpus (2)

• An interacting particle model and a Pieri-type formula for the orthogonal group
• A (2+1)-dimensional Gaussian field as fluctuations of quantum random walks on quantum groups