no. 1
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

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. 
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     title = {On the {Iwahori} {Weyl} group},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {117--124},
     year = {2016},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {144},
     number = {1},
     doi = {10.24033/bsmf.2708},
     mrnumber = {3481263},
     zbl = {1342.20051},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/bsmf.2708/}
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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

Bourbaki, N. Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968 | MR | Zbl

Bruhat, F.; Tits, J. Groupes réductifs sur un corps local, Publ. Math. IHÉS, Volume 41 (1972), pp. 5-251 (ISSN: 0073-8301) | MR | Zbl | Numdam | DOI

Bruhat, F.; Tits, J. Groupes réductifs sur un corps local. II. Schémas en groupes. Existence d'une donnée radicielle valuée, Publ. Math. IHÉS, Volume 60 (1984), pp. 197-376 (ISSN: 0073-8301) | Numdam | MR | Zbl

Haines, T.; Rapoport, M. On parahoric subgroups, Adv. Math., Volume 219 (2008), pp. 188-198 (appendix to [6] ) (ISSN: 0001-8708) | MR | DOI

Kottwitz, Robert E. Isocrystals with additional structure. II, Compositio Math., Volume 109 (1997), pp. 255-339 (ISSN: 0010-437X) | MR | Zbl | DOI

Pappas, G.; Rapoport, M. Twisted loop groups and their affine flag varieties, Adv. Math., Volume 219 (2008), pp. 118-198 (ISSN: 0001-8708) | MR | Zbl | DOI

Tits, J., Automorphic forms, representations and L -functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1 (Proc. Sympos. Pure Math., XXXIII), Amer. Math. Soc., Providence, R.I., 1979, pp. 29-69 | MR | Zbl

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