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Comparaison d’intégrales orbitales pour des Groupesp-adiques

In: Proceedings of the International Congress of Mathematicians

Author

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  • Jean-Loup Waldspurger

    (Université Paris 7, CNRS)

Abstract

Zusammenfassung (a) Soient F un corps local non archimédien de caractéristique nulle, à corps résiduel fini, et G un groupe réductif connexe défini sur F. Munissons G(F) d’une mesure de Haar. Plus généralement, pour tout sous-groupe fermé unimodulaire H ⊂ G(F), munissons H d’une mesure de Haar et H\G(F) de la mesure quotient. Notons $$ C_c^\infty $$ (G(F)) l’espace des fonctions sur G(F), à valeurs complexes, localement constantes et à support compact. Pourf ∈ $$ C_c^\infty $$ (G(F)) etx ∈G(F), posons $$ {\phi ^G}(x,f) = {\smallint _{{Z_G}(x) \circ (F)\backslash G(F)}}f({y^{ - 1}}xy)dy$$ oùZ G (x)○ est la composante neutre du commutant de x dans G. L’intégrale est absolument convergente ([Rao]). Fixons un ensemble de représentations U G ⊂ G(F) des classes de conjugaison unipotentes, pour la conjugaison par G(F).

Suggested Citation

  • Jean-Loup Waldspurger, 1995. "Comparaison d’intégrales orbitales pour des Groupesp-adiques," Springer Books, in: S. D. Chatterji (ed.), Proceedings of the International Congress of Mathematicians, pages 807-816, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9078-6_74
    DOI: 10.1007/978-3-0348-9078-6_74
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