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Journal of Theoretical Probability

, Volume 31, Issue 3, pp 1411–1428 | Cite as

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

  • Jeffrey Kuan
Article
  • 66 Downloads

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.

Keywords

Noncommutative random walk Littlewood–Richardson coefficients Group von Neumann algebra Representation theory 

Mathematics Subject Classification (2010)

60B99 60C05 60J10 60J27 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Columbia UniversityNew YorkUSA

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