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Ordering the Representations of ${{S}_{n}}$ Using the Interchange Process

Published online by Cambridge University Press:  20 November 2018

Gil Alon
Affiliation:
Division of Mathematics, The Open University of Israel, Raanana 43107, Israel e-mail: gilal@openu.ac.il
Gady Kozma
Affiliation:
Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel e-mail: gadyk@weizmann.ac.il
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2013

References

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