2003/04/08 by François Courtès, Francois Courtes, Courtes, Francois
Mathematics · #22E35 (primary) 20G40 (secondary) #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20G40 #msc:22E35
paper · pdf · doi:10.48550/arxiv.math/0304109
124 pages, in French
arxiv created 2003/04/08 · openalex publication_date 2003/04/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F be a nonarchimedean local field, and G the group of F-points of a c onnected quasisplit reductive group defined on F; in this paper, we will study the distributions on G which are invariant by conjugation, and the vector spa ce of their restrictions to the Hecke algebra H of the functions on G with compact support and biinvariant by a given Iwahori subgroup I. It is first shown that such a distribution on H is entirely determined by its restriction to the finite-diimensional subspace of H containing the elements with support in the union of the parahoric subgroups of G contai ning I; this property is then used, by establishing similar results on finite groups, to show, with some conditions on G, that this space is generated both by some semisimple orbital integrals and by unipotent integrals.