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Ordering the Representations of $S_n$ Using the Interchange Process

  Published:2011-07-15
 Printed: Mar 2013
  • Gil Alon,
    Division of Mathematics, The Open University of Israel, Raanana 43107, Israel
  • Gady Kozma,
    Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
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Abstract

Inspired by Aldous' conjecture for the spectral gap of the interchange process and its recent resolution by Caputo, Liggett, and Richthammer, we define an associated order $\prec$ on the irreducible representations of $S_n$. Aldous' conjecture is equivalent to certain representations being comparable in this order, and hence determining the ``Aldous order'' completely is a generalized question. We show a few additional entries for this order.
Keywords: Aldous' conjecture, interchange process, symmetric group, representations Aldous' conjecture, interchange process, symmetric group, representations
MSC Classifications: 82C22, 60B15, 43A65, 20B30, 60J27, 60K35 show english descriptions Interacting particle systems [See also 60K35]
Probability measures on groups or semigroups, Fourier transforms, factorization
Representations of groups, semigroups, etc. [See also 22A10, 22A20, 22Dxx, 22E45]
Symmetric groups
Continuous-time Markov processes on discrete state spaces
Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
82C22 - Interacting particle systems [See also 60K35]
60B15 - Probability measures on groups or semigroups, Fourier transforms, factorization
43A65 - Representations of groups, semigroups, etc. [See also 22A10, 22A20, 22Dxx, 22E45]
20B30 - Symmetric groups
60J27 - Continuous-time Markov processes on discrete state spaces
60K35 - Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
 

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