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

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  • Jeffrey Kuan

    (Columbia University)

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.

Suggested Citation

  • Jeffrey Kuan, 2018. "Two Constructions of Markov Chains on the Dual of U(n)," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1411-1428, September.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:3:d:10.1007_s10959-017-0757-1
    DOI: 10.1007/s10959-017-0757-1
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