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Two Constructions of Markov Chains on the Dual of U(n)

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Abstract

We provide two new constructions of Markov chains which had previously arisen from the representation theory of \(U(\infty )\). 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 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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  1. Columbia University, New York, NY, USA

    Jeffrey Kuan

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  1. Jeffrey Kuan
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Correspondence to Jeffrey Kuan.

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Kuan, J. Two Constructions of Markov Chains on the Dual of U(n). J Theor Probab 31, 1411–1428 (2018). https://doi.org/10.1007/s10959-017-0757-1

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  • DOI: https://doi.org/10.1007/s10959-017-0757-1

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