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Representation Theory

ISSN 1088-4165

 

 

Conjugacy classes of involutions and Kazhdan-Lusztig cells


Authors: Cédric Bonnafé and Meinolf Geck
Journal: Represent. Theory 18 (2014), 155-182
MSC (2000): Primary 20C08; Secondary 20F55
Published electronically: July 22, 2014
MathSciNet review: 3233059
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Abstract: According to an old result of Schützenberger, the involutions in a given two-sided cell of the symmetric group $ \mathfrak{S}_n$ are all conjugate. In this paper, we study possible generalizations of this property to other types of Coxeter groups. We show that Schützenberger's result is a special case of a general result on ``smooth'' two-sided cells. Furthermore, we consider Kottwitz's conjecture concerning the intersections of conjugacy classes of involutions with the left cells in a finite Coxeter group. Our methods lead to a proof of this conjecture for classical types which, combined with further recent work, settles this conjecture in general.


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Cédric Bonnafé
Affiliation: Institut de Mathématiques et de Modélisation de Montpellier (CNRS: UMR 5149), Université Montpellier 2, Case Courrier 051, Place Eugène Bataillon, 34095 Montpellier Cedex, France
Email: cedric.bonnafe@math.univ-montp2.fr

Meinolf Geck
Affiliation: IAZ - Lehrstuhl für Algebra, Universität Stuttgart, Pfaffenwaldring 57, D–70569 Stuttgart, Germany
Email: meinolf.geck@mathematik.uni-stuttgart.de

DOI: https://doi.org/10.1090/S1088-4165-2014-00456-4
Received by editor(s): January 28, 2013
Received by editor(s) in revised form: July 1, 2014
Published electronically: July 22, 2014
Article copyright: © Copyright 2014 American Mathematical Society