Vol. 197, No. 1, 2001

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Decomposition of double cosets in p-adic groups

Joshua M. Lansky

Vol. 197 (2001), No. 1, 97–117

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.

Received: 22 April 1999
Revised: 24 August 1999
Published: 1 January 2001
Joshua M. Lansky
Department of Mathematics
University of Rochester
Rochester, New York 14627