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
We give a detailed calculation of the Hochschild and cyclic homology of the algebra of locally constant, compactly supported functions on a reductive -adic group . 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.
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