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Comptes Rendus Mathématique
Volume 335, n° 1
pages 11-16 (2002)
Doi : S1631-073X(02)02421-4
Received : 20 Mars 2002 ; 
Formules de caractères pour des représentations irréductibles du groupe symplectique en caractéristique p
Character formulas of irreducible representations of the symplectic group in prime characteristic
 

Sébastien Foulle
Institut Girard Desargues, Université Lyon I, 21, avenue Claude Bernard, 69622 Villeurbanne cedex, France 

Note présentée par Michel Duflo

Résumé

On obtient des formules de caractères pour certaines représentations irréductibles du groupe Sp(2m,Fp) en égale caractéristique. Ces formules peuvent sortir du domaine de validité de la conjecture de Lusztig, ainsi pour tout s⩽p−32 on a une formule de caractère pour L(sωm). On démontre ces résultats à l'aide de la théorie des paires duales et de la formule modulaire de Verlinde. Pour citer cet article : S. Foulle, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 11-16.

The full text of this article is available in PDF format.
Abstract

We obtain character formulas of some irreducible representations of Sp(2m,Fp) in equal characteristic. These formulas can be outside the validity domain of the Lusztig conjecture, for instance for all s⩽p−32 we get the character of the irreducible representation with highest weight m . The proof uses dual pairs theory and the modular Verlinde formula. To cite this article: S. Foulle, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 11-16.

The full text of this article is available in PDF format.


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