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Theses

Sur le support unipotent des faisceaux-caractères

Abstract : Let G be a connected reductive algebraic group with connected centre over a finite field of characteristic p>0. We put on this structure a Frobenius map F and we note G^F the set of the elements of G which are fixed by the action of G : G^F is a finite group. We suppose that the characteristic p is good for G.

Then, we define an application Phi_G from the set of the special conjugaison classes of G^* to the set of the unipotent classes of G. This application describes the unipotent support of the different classes of character sheaves defined on G.

On the other hand, with the Springer correspondence, we define some invariants, for example the d-invariants, for the characters of a Weyl group W. We have studied the link between the induction of special characters of certain subgroups of W and the d-invariants. With these results, we show that Phi_G, restricted to certain special classes of G^* is surjective. We have also showed that the Frobenius stability can be introduced in this result.

We deduced from that two results. The first one is a strong link between the restrictions to the unipotent elements of character sheaves of certain classes and different local irreducible G-equivariant systems on the unipotent classes of G.

The second result is a proof of a Kawanaka conjecture on the generalized Gelfand-Graev characters : they constitute a base of the Z-module of the virtual characters of G^F with unipotent support.
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https://tel.archives-ouvertes.fr/tel-00012071
Contributor : David Hezard <>
Submitted on : Friday, March 31, 2006 - 12:33:48 PM
Last modification on : Wednesday, November 20, 2019 - 2:44:36 AM
Long-term archiving on: : Saturday, April 3, 2010 - 10:10:09 PM

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  • HAL Id : tel-00012071, version 1

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David Hezard. Sur le support unipotent des faisceaux-caractères. Mathématiques [math]. Université Claude Bernard - Lyon I, 2004. Français. ⟨tel-00012071⟩

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