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Transformation Groups

, Volume 20, Issue 3, pp 615–663 | Cite as

DIMENSION DES FIBRES DE SPRINGER AFFINES POUR LES GROUPES

  • ALEXIS BOUTHIER
Article

Abstract

This article establishes a dimension formula for a group version of affine Springer fibers. We follow the method initiated by Bezrukavnikov in the case of Lie algebras. It consists in the introduction of a big enough regular open subset, with the same dimension as the affine Springer fiber. We show that, in the case of groups, such a regular open subset with analogous properties exists. Its construction needs the introduction of the Vinberg semi-group VG, for which we study an adjoint quotient χ+ and extend for χ+ the results previously established by Steinberg.

Keywords

Nous Avons Compacti Cation Nous Allons Nous Obtenons Regular Open Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Résumé

Cet article établit une formule de dimension pour les fibres de Springer affines dans le cas des groupes. On suit la méthode initiée par Bezrukavnikov dans le cas des algébres de Lie. Elle consiste en l'introduction d'un ouvert régulier suffisamment gros dont on montre qu'il est de même dimension que la fibre de Springer affine entiére. On montre que dans le cas des groupes, un tel ouvert régulier avec des propriétés analogues existe. Sa construction passe par l'introduction du semi-groupe de Vinberg VG pour lequel nous étudions un morphisme ≪polynôme caractéristique≫ et étendons les résultats précedemment établis par Steinberg pour les groupes.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Université Paris-Sud UMR 8628Orsay CedexFrance

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