Geodesic
Unipotent Orbital Integrals of Hecke Functions for GL(n)
Canadian journal of mathematics, Tome 46 (1994) no. 2, pp. 308-323

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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 u 1,..., 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).
DOI : 10.4153/CJM-1994-015-3
Mots-clés : 22E35 
Herb, Rebecca A. Unipotent Orbital Integrals of Hecke Functions for GL(n). Canadian journal of mathematics, Tome 46 (1994) no. 2, pp. 308-323. doi: 10.4153/CJM-1994-015-3
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