On Kottwitz' conjecture for twisted involutions

2012/06/03 by Meinolf Geck, Geck, Meinolf · 1 citation
Mathematics · #20C08 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1206.0443

openalex publication_date 2012/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Kottwitz' conjecture is concerned with the intersections of Kazhdan--Lusztig cells with conjugacy classes of involutions in finite Coxeter groups. In joint work with Bonnafé, we have recently found a way to prove this conjecture for groups of type B_n and D_n. The argument for type D_n relies on two ingredients which were used there without proof: (1) a strengthened version of the "branching rule" and (2) the consideration of "\diamond-twisted" involutions where \diamond is a graph automorphism. In this paper we deal with (1), (2) and complete the argument for type D_n; moreover, we establish Kottwitz' conjecture for \diamond-twisted involutions in all cases where \diamond is non-trivial.

Citations

• A bar operator for involutions in a Coxeter group

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• Lie algebras generated by reflections in types BCD

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