On the lowest two-sided cell in affine Weyl groups

2007/03/26 by Jérémie Guilhot, Jeremie Guilhot, Guilhot, Jeremie
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.math/0703764

18 pages, 1 figure, final version (minor changes). To appear in Representation theory

openalex publication_date 2007/03/26 · arxiv created 2008/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Bremke and Xi determined the lowest two-sided cell for affine Weyl groups with unequal parameters and showed that it consists of at most |W₀| left cells where W₀ is the associated finite Weyl group. We prove that this bound is exact. Previously, this was known in the equal parameter case and when the parameters were coming from a graph automorphism. Our argument uniformly works for any choice of parameters.

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