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arXiv · 1212.2939

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

Jeffrey Kuan
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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.

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BibTeXRIS

Jeffrey Kuan. 2017-04-09. Two constructions of Markov chains on the dual of U(n). https://doi.org/10.1007/s10959-017-0757-1

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