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.

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