Local character expansions

Dan Barbasch, Allen Moy

Type: Article

Publication Date: 1997-01-01

Citations: 25

DOI: https://doi.org/10.1016/s0012-9593(97)89931-4

Abstract

Abstract In this paper the authors develop a method to compute the local character expansion of a depth zero representation of a p-adic group. The main idea is to use the generalized Gelfand-Graev characters for finite groups as test functions to plug into the character formula. This is possible due to results of Waldspurger on the validity of the local character expansion in a large enough neighborhood of the identity. The method leads to a classification of the unipotent orbits in terms of parahoric subalgebras.

Locations

Annales Scientifiques de l École Normale Supérieure - View
French digital mathematics library (Numdam) - View - PDF

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+	Fourier transforms of nilpotently supported invariant functions on a simple lie algebra over a finite field	1982	Noriaki Kawanaka
+	Jacquet functors and unrefined minimal K-types	1996	Allen Moy Gopal Prasad
+ PDF Chat	Homogénéité de certaines distributions sur les groupes p-adiques	1995	J. L. Waldspurger
+ PDF Chat	Unrefined minimal K-types forp-adic groups	1994	Allen Moy Gopal Prasad
+	The Fourier transform and germs of characters (case of Gl n over ap-adic field)	1974	Roger Howe
+	A unipotent support for irreducible representations	1992	George Lusztic
+ PDF Chat	Quelques questions sur les intégrales orbitales unipotentes et les algèbres de Hecke	1996	Jean-Loup Waldspurger
+	An application of the building to orbital integrals	1980	Jonathan David Rogawski
+	Finite groups of Lie type	1985	Meinolf Geck