Decomposition of double cosets in p-adic groups

Joshua M. Lansky

Vol. 197 (2001), No. 1, 97–117

DOI: 10.2140/pjm.2001.197.97

Abstract

Let G be a split group over a locally compact field F with non-trivial discrete valuation. Employing the structure theory of such groups and the theory of Coxeter groups, we obtain a general formula for the decomposition of double cosets P₁σP₂ of subgroups P₁,P₂ ⊂ G(F) containing an Iwahori subgroup into left cosets of P₂. When P₁ and P₂ are the same hyperspecial subgroup, we use this result to derive a formula of Iwahori for the degrees of elements of the spherical Hecke algebra.

Milestones

Received: 22 April 1999

Revised: 24 August 1999

Published: 1 January 2001