Spherical roots of spherical varieties
Annales de l'Institut Fourier, Volume 64 (2014) no. 6, p. 2503-2526

Brion proved that the valuation cone of a complex spherical variety is a fundamental domain for a finite reflection group, called the little Weyl group. The principal goal of this paper is to generalize this theorem to fields of characteristic unequal to 2. We also prove a weaker version which holds in characteristic 2, as well. Our main tool is a generalization of Akhiezer’s classification of spherical varieties of rank 1.

Brion a prouvé que le cône de valuations d’une variété sphérique complexe est un domaine fondamental pour un groupe de réflexion finie, appelée petit groupe de Weyl. L’objectif principal de cet article est de généraliser ce théorème à des corps de caractéristique différent de 2. Nous prouvons aussi une version plus faible qui tient en caractéristique 2. Notre outil principal est une généralisation du classement d’Akhiezer des variétés sphériques de rang 1.

DOI : https://doi.org/10.5802/aif.2919
Classification:  14M27,  14L30,  14G17
Keywords: Spherical varieties, spherical roots, homogeneous varieties, fields of positive characteristic
@article{AIF_2014__64_6_2503_0,
     author = {Knop, Friedrich},
     title = {Spherical roots of spherical varieties},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {6},
     year = {2014},
     pages = {2503-2526},
     doi = {10.5802/aif.2919},
     mrnumber = {3331173},
     zbl = {06387346},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_6_2503_0}
}
Knop, Friedrich. Spherical roots of spherical varieties. Annales de l'Institut Fourier, Volume 64 (2014) no. 6, pp. 2503-2526. doi : 10.5802/aif.2919. http://www.numdam.org/item/AIF_2014__64_6_2503_0/

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