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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
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.