Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras

Details Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras

2000-08-16

arxiv.org/abs/math/0008133v1

Mathematics

Representation Theory

AMS-Latex, 27 pages

Scientific paper

We give a detailed calculation of the Hochschild and cyclic homology of the algebra $\CIc(G)$ of locally constant, compactly supported functions on a reductive p-adic group G. We use these calculations to extend to arbitrary elements the definition the higher orbital integrals introduced in \cite{Blanc-Brylinski} for regular semisimple elements. Then we extend to higher orbital integrals some results of Shalika. We also investigate the effect of the ``induction morphism'' on Hochschild homology.

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