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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832565009184456704 |
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| author | Victor Nistor |
| author_facet | Victor Nistor |
| author_sort | Victor Nistor |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1ceb2c6076454be6bc6bcd17c5a3549a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1ceb2c6076454be6bc6bcd17c5a3549a2025-02-03T01:09:31ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0126312916010.1155/S0161171201020038Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebrasVictor Nistor0Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USAWe 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.http://dx.doi.org/10.1155/S0161171201020038 |
| spellingShingle | Victor Nistor Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras International Journal of Mathematics and Mathematical Sciences |
| title | Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras |
| title_full | Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras |
| title_fullStr | Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras |
| title_full_unstemmed | Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras |
| title_short | Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras |
| title_sort | higher orbital integrals shalika germs and the hochschild homology of hecke algebras |
| url | http://dx.doi.org/10.1155/S0161171201020038 |
| work_keys_str_mv | AT victornistor higherorbitalintegralsshalikagermsandthehochschildhomologyofheckealgebras |