On the spectral gap of some Cayley graphs on the Weyl group W(B_n)

2018/07/31 by Cesi, Filippo · 1 citation
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paper · doi:10.48550/arxiv.1807.11833

Abstract

The Laplacian of a (weighted) Cayley graph on the Weyl group W(B_n) is a N× N matrix with N = 2ⁿ n! equal to the order of the group. We show that for a class of (weighted) generating sets, its spectral gap (lowest nontrivial eigenvalue), is actually equal to the spectral gap of a 2n × 2n matrix associated to a 2n-dimensional permutation representation of W_n. This result can be viewed as an extension to W(B_n) of an analogous result valid for the symmetric group, known as `Aldous' spectral gap conjecture', proven in 2010 by Caputo, Liggett and Richthammer.

Cited by

• The Aldous property for normal Cayley graphs on symmetric groups

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