Frobenius contraction of G -modules

Michel Gros[1]; Masaharu Kaneda[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)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 6, page 2507-2542
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Gros, Michel, and Kaneda, Masaharu. "Contraction par Frobenius de $G$-modules." Annales de l’institut Fourier 61.6 (2011): 2507-2542. <http://eudml.org/doc/219768>.

@article{Gros2011,
abstract = {Soit $G$ un groupe algébrique semi-simple simplement connexe défini sur un corps algébriquement clos $\mathbb\{k\}$ 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.},
affiliation = {Université de Rennes I IRMAR Campus de Beaulieu 35042 Rennes cedex (France); Osaka City University Department of Mathematics 3-3-138 Sugimoto Sumiyoshi-ku Osaka 558-8585 (Japan)},
author = {Gros, Michel, Kaneda, Masaharu},
journal = {Annales de l’institut Fourier},
keywords = {Frobenius splitting; flag variety; Schubert variety; distribution algebra},
language = {fre},
number = {6},
pages = {2507-2542},
publisher = {Association des Annales de l’institut Fourier},
title = {Contraction par Frobenius de $G$-modules},
url = {http://eudml.org/doc/219768},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Gros, Michel
AU - Kaneda, Masaharu
TI - Contraction par Frobenius de $G$-modules
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 6
SP - 2507
EP - 2542
AB - Soit $G$ un groupe algébrique semi-simple simplement connexe défini sur un corps algébriquement clos $\mathbb{k}$ 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.
LA - fre
KW - Frobenius splitting; flag variety; Schubert variety; distribution algebra
UR - http://eudml.org/doc/219768
ER -

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