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

Victor Nistor

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 26, 1-32

Abstract:

We give a detailed calculation of the Hochschild and cyclic homology of the algebra 𝒞 c ∞ ( 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 of the higher orbital integrals introduced by Blanc and Brylinski (1992) for regular semi-simple elements. Then we extend to higher orbital integrals some results of Shalika (1972). We also investigate the effect of the “induction morphism” on Hochschild homology.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:705019

DOI: 10.1155/S0161171201020038

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