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

Victor Nistor
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Abstract

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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Victor Nistor. 2000-08-16. Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras. https://arxiv.org/abs/math/0008133

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