International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2001 / Article

Open Access

Volume 26 |Article ID 705019 | https://doi.org/10.1155/S0161171201020038

Victor Nistor, "Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras", International Journal of Mathematics and Mathematical Sciences, vol. 26, Article ID 705019, 32 pages, 2001. https://doi.org/10.1155/S0161171201020038

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

Received01 Mar 2001

Abstract

We give a detailed calculation of the Hochschild and cyclic homology of the algebra 𝒞c(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.

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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