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 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 introduce...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201020038 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |