Sur le groupe de Weyl-Iwahori

On the Iwahori Weyl group

Timo Richarz
Sur le groupe de Weyl-Iwahori
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  • Année : 2016
  • Fascicule : 1
  • Tome : 144
  • Format : Électronique
  • Langue de l'ouvrage :
  • Class. Math. : 02F55, 20G25.
  • Pages : 117-124
  • DOI : 10.24033/bsmf.2708
Let F be a discretely valued complete field with valuation ring $\mathcal {O}_F$ and perfect residue field $k$ of cohomological dimension $\leq 1$. In this paper, we generalize the Bruhat decomposition in Bruhat and Tits [?] 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 [?] 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)].
Affine Weyl group, Reductive groups over local fields, Bruhat decomposition.