no. 6
Contraction par Frobenius de G-modules
Gros, Michel1 ; Kaneda, Masaharu2
1 Université de Rennes I IRMAR Campus de Beaulieu 35042 Rennes cedex (France)
2 Osaka City University Department of Mathematics 3-3-138 Sugimoto Sumiyoshi-ku Osaka 558-8585 (Japan)
Annales de l'Institut Fourier, Tome 61 (2011) no. 6, pp. 2507-2542.

Soit G un groupe algébrique semi-simple simplement connexe défini sur un corps algébriquement clos 𝕜 de caractéristique positive. Nous donnons une nouvelle preuve de l’existence d’un scindage de Frobenius de la variété des drapeaux de G ainsi que de la nature G-équivariante de celui-ci. L’outil principal est un scindage de l’endomorphisme de Frobenius défini sur toute l’algèbre des distributions de G qui permet de « détordre » la structure des G-modules.

Let G be a simply connected semisimple algebraic group over an algebraically closed field 𝕜 of positive characteristic. We will give a new proof of the Frobenius splitting of the flag variety of G and of its G-equivariant nature. The key tool is a newly found splitting of the Frobenius endomorphism on the algebra of distributions of G allowing us to “untwist” the structure of G-modules.

DOI : 10.5802/aif.2681
Classification : 14M15, 13A35, 17B10, 20G05, 20G10
Mot clés : scindage de Frobenius, variété des drapeaux, variété de Schubert, algèbre des distributions
Keywords: Frobenius splitting, flag variety, Schubert variety, distribution algebra

Gros, Michel 1 ; Kaneda, Masaharu 2

1 Université de Rennes I IRMAR Campus de Beaulieu 35042 Rennes cedex (France)
2 Osaka City University Department of Mathematics 3-3-138 Sugimoto Sumiyoshi-ku Osaka 558-8585 (Japan) 
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     title = {Contraction par {Frobenius} de $G$-modules},
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Gros, Michel; Kaneda, Masaharu. Contraction par Frobenius de $G$-modules. Annales de l'Institut Fourier, Tome 61 (2011) no. 6, pp. 2507-2542. doi : 10.5802/aif.2681. https://aif.centre-mersenne.org/articles/10.5802/aif.2681/

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