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

Jeffrey Kuan ()
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Jeffrey Kuan: Columbia University

Journal of Theoretical Probability, 2018, vol. 31, issue 3, 1411-1428

Abstract: Abstract We provide two new constructions of Markov chains which had previously arisen from the representation theory of $$U(\infty )$$ U ( ∞ ) . 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.

Keywords: Noncommutative random walk; Littlewood–Richardson coefficients; Group von Neumann algebra; Representation theory; 60B99; 60C05; 60J10; 60J27 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-017-0757-1

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