Mathematics – Representation Theory
Scientific paper
2008-10-28
Mathematics
Representation Theory
27 pages
Scientific paper
Nous obtenons une formule pour les valeurs de la fonction caract\'eristique d'un faisceau caract\`ere en fonction de la th\'eorie des repr\'esentations de certains groupes finis, li\'es au groupe de Weyl. Cette formule, qui g\'en\'eralise des r\'esultats ant\'erieurs de M{\oe}glin et de Waldspurger, d\'epend de la connaissance de certains sous-groupes r\'eductifs admettant un faisceau caract\`ere cuspidal. Dans un second temps, afin de rendre la formule plus explicite dans le cas d'un groupe quasi-simple, nous d\'eterminons ces sous-groupes \`a conjugaison pr\`es. We obtain a formula for the values of the characteristic function of a character sheaf, in terms of the representation theory of certain finite groups related to the Weyl group. This formula, a generalization of previous results due to M{\oe}glin and Waldspurger, depends on knowledge of certain reductive subgroups that admit cuspidal character sheaves. For quasi-simple groups, we make the formula truly explicit by determining all such subgroups upto conjugation.
Achar Pramod N.
Aubert Anne-Marie
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