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Unipotent Orbital Integrals of Hecke Functions for GL(n)

Published online by Cambridge University Press:  20 November 2018

Rebecca A. Herb
Rebecca A. Herb*
Affiliation:
Department of Mathematics University of Maryland College Park, Maryland 20742 U.S.A.
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Abstract

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Let G = GL(n, F) where F is a p-adic field, and let 𝓗(G) denote the Hecke algebra of spherical functions on G. Let u1,..., up denote a complete set of representatives for the unipotent conjugacy classes in G. For each 1 ≤ i ≤ p, let μi be the linear functional on such that μi(f) is the orbital integral of f over the orbit of ui. Waldspurger proved that the μi, 1 ≤ i ≤ p, are linearly independent. In this paper we give an elementary proof of Waldspurger's theorem which provides concrete information about the Hecke functions needed to separate orbits. We also prove a twisted version of Waldspurger's theorem and discuss the consequences for SL(n, F).

Keywords

22E35
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 2 , 01 April 1994 , pp. 308 - 323
Copyright
Copyright © Canadian Mathematical Society 1994

References

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