Geodesic
On Kottwitz's Conjecture for Twisted Involutions
Journal of Lie theory, Tome 25 (2015) no. 2, pp. 395-429
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Motivated by problems on nilpotent orbital integrals for real Lie groups, Kottwitz (2000) formulated a conjecture concerning the relationship between Kazhdan-Lusztig cells of a finite Coxeter group $W$ and its conjugacy classes of $\diamond$-twisted involutions, where $\diamond$ is an involutory graph automorphism of $W$. In this paper, we study this relationship in type $D_n$ and all cases where $\diamond$ is non-trivial. Combined with work of Kottwitz himself, Casselmann, Marberg, and joint work of Bonnaf\'e, Halls and the author, this completes the proof of Kottwitz's Conjecture for all $W,\,\diamond$.
Classification : 20F55, 20G40, 22E50
Mots-clés : Coxeter groups, twisted involutions, Kazhdan-Lusztig cells 
@article{JLT_2015_25_2_JLT_2015_25_2_a4,
     author = {M. Geck},
     title = {On {Kottwitz's} {Conjecture} for {Twisted} {Involutions}},
     journal = {Journal of Lie theory},
     pages = {395--429},
     year = {2015},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2015_25_2_JLT_2015_25_2_a4/}
}
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M. Geck. On Kottwitz's Conjecture for Twisted Involutions. Journal of Lie theory, Tome 25 (2015) no. 2, pp. 395-429. http://geodesic.mathdoc.fr/item/JLT_2015_25_2_JLT_2015_25_2_a4/