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Article Dans Une Revue Representation theory : An Electronic Journal of the American Mathematical Society Année : 2014

Conjugacy classes of involutions and Kazhdan-Lusztig cells

Résumé

According to an old result of Schützenberger, the involutions in a given two-sided cell of the symmetric group $\SG_n$ are all conjugate. In this paper, we study possible generalisations 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' 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; combined with previous work, this leaves type $E_8$ as the only remaining open case.
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Dates et versions

hal-00698613 , version 1 (17-05-2012)
hal-00698613 , version 2 (08-06-2012)

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Cédric Bonnafé, Meinolf Geck. Conjugacy classes of involutions and Kazhdan-Lusztig cells. Representation theory : An Electronic Journal of the American Mathematical Society, 2014, 18, pp.155-182. ⟨10.1090/S1088-4165-2014-00456-4⟩. ⟨hal-00698613v2⟩
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