The Spherical Hecke algebra, partition functions, and motivic integration
| Autor: | Thomas C. Hales, Jorge E. Cely, William Casselman |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Transfer principle
Pure mathematics Hecke algebra Mathematics - Number Theory Group (mathematics) Applied Mathematics General Mathematics Mathematics::Number Theory 010102 general mathematics MathematicsofComputing_GENERAL Function (mathematics) Fundamental lemma Reductive group 01 natural sciences Matrix (mathematics) 0103 physical sciences FOS: Mathematics 010307 mathematical physics Number Theory (math.NT) 0101 mathematics Representation Theory (math.RT) Motivic integration Mathematics::Representation Theory Mathematics - Representation Theory Mathematics |
| Popis: | This article gives a proof of the Langlands-Shelstad fundamental lemma for the spherical Hecke algebra for every unramified p-adic reductive group G in large positive characteristic. The proof is based on the transfer principle for constructible motivic integration. To carry this out, we introduce a general family of partition functions attached to the complex L-group of the unramified p-adic group G. Our partition functions specialize to Kostant's q-partition function for complex connected groups and also specialize to the Langlands L-function of a spherical representation. These partition functions are used to extend numerous results that were previously known only when the L-group is connected (that is, when the p-adic group is split). We give explicit formulas for branching rules, the inverse of the weight multiplicity matrix, the Kato-Lusztig formula for the inverse Satake transform, the Plancherel measure, and Macdonald's formula for the spherical Hecke algebra on a non-connected complex group (that is, non-split unramified p-adic group). 45 pages |
| Databáze: | OpenAIRE |
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