Geodesic
On the Iwahori Weyl group
[Sur le groupe de Weyl-Iwahori]
Bulletin de la Société Mathématique de France, Tome 144 (2016) no. 1, pp. 117-124

Voir la notice de l'article provenant de la source Numdam

Let F be a discretely valued complete field with valuation ring 𝒪F and perfect residue field k of cohomological dimension ≤1. In this paper, we generalize the Bruhat decomposition in Bruhat and Tits [Publ. Math. IHÉS 60 (1984)] from the case of simply connected F-groups to the case of arbitrary connected reductive F-groups. If k is algebraically closed, Haines and Rapoport [Adv. Math. 219 (2008)] define the Iwahori-Weyl group, and use it to solve this problem. Here we define the Iwahori-Weyl group in general, and relate our definition of the Iwahori-Weyl group to that of [Adv. Math. 219 (2008)].

Publié le :
DOI : 10.24033/bsmf.2708
Classification : 02F55, 20G25
Keywords: Affine Weyl group, Reductive groups over local fields, Bruhat decomposition. 
@article{BSMF_2016__144_1_117_0,
     author = {Richarz, Timo},
     title = {On the {Iwahori} {Weyl} group},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {117--124},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {144},
     number = {1},
     year = {2016},
     doi = {10.24033/bsmf.2708},
     mrnumber = {3481263},
     zbl = {1342.20051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.24033/bsmf.2708/}
}
TY  - JOUR
AU  - Richarz, Timo
TI  - On the Iwahori Weyl group
JO  - Bulletin de la Société Mathématique de France
PY  - 2016
SP  - 117
EP  - 124
VL  - 144
IS  - 1
PB  - Société mathématique de France
UR  - http://geodesic.mathdoc.fr/articles/10.24033/bsmf.2708/
DO  - 10.24033/bsmf.2708
LA  - en
ID  - BSMF_2016__144_1_117_0
ER  - 
%0 Journal Article
%A Richarz, Timo
%T On the Iwahori Weyl group
%J Bulletin de la Société Mathématique de France
%D 2016
%P 117-124
%V 144
%N 1
%I Société mathématique de France
%U http://geodesic.mathdoc.fr/articles/10.24033/bsmf.2708/
%R 10.24033/bsmf.2708
%G en
%F BSMF_2016__144_1_117_0
Richarz, Timo. On the Iwahori Weyl group. Bulletin de la Société Mathématique de France, Tome 144 (2016) no. 1, pp. 117-124. doi: 10.24033/bsmf.2708

Cité par Sources :