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International Journal of Mathematics and Mathematical Sciences
Volume 26, Issue 3, Pages 129-160

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

Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA

Received 1 March 2001

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.


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.