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Ordering the Representations of $S_n$ Using the Interchange Process |
Canad. Math. Bull. 56(2013), 13-30
Published:2011-07-15
Printed: Mar 2013
Printed: Mar 2013
- Gil Alon,
- Gady Kozma,
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 |
| MSC Classifications: |
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] |