On the determination of Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters

2007/02/09 by Jérémie Guilhot, Jeremie Guilhot, Guilhot, Jeremie · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.math/0702272

22 pages, 2 figures, the revised version contains additional reference and some rewritting. Submitted

openalex publication_date 2007/02/09 · arxiv created 2007/07/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let W be a Coxeter group and L be a weight function on W. Following Lusztig, we have a corresponding decomposition of W into left cells, which have important applications in representation theory. We study the case where W is an affine Weyl group of type G₂. Using explicit computation with \textsfCHEVIE, we show that (1) there are only finitely many possible decompositions into left cells and (2) the number of left cells is finite in each case, thus confirming some of Lusztig's conjectures in this case. For the proof, we show some equalities on the Kazhdan-Lusztig polynomials which hold for any affine Weyl groups.

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