Journal of Lie Theory

no. 2
On Kottwitz's Conjecture for Twisted Involutions
Journal of Lie Theory, Volume 25 (2015) no. 2, pp. 395-429
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 $W,\,\diamond$.
DOI: 10.5802/jolt.842
Classification: 20F55, 20G40, 22E50
Keywords: Coxeter groups, twisted involutions, Kazhdan-Lusztig cells 
@article{JOLT_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},
     doi = {10.5802/jolt.842},
     zbl = {1331.20049},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.842/}
}
TY  - JOUR
AU  - M. Geck
TI  - On Kottwitz's Conjecture for Twisted Involutions
JO  - Journal of Lie Theory
PY  - 2015
SP  - 395
EP  - 429
VL  - 25
IS  - 2
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.842/
DO  - 10.5802/jolt.842
ID  - JOLT_2015_25_2_a4
ER  - 
%0 Journal Article
%A M. Geck
%T On Kottwitz's Conjecture for Twisted Involutions
%J Journal of Lie Theory
%D 2015
%P 395-429
%V 25
%N 2
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.842/
%R 10.5802/jolt.842
%F JOLT_2015_25_2_a4
M. Geck. On Kottwitz's Conjecture for Twisted Involutions. Journal of Lie Theory, Volume 25 (2015) no. 2, pp. 395-429. doi: 10.5802/jolt.842

Cited by Sources: