تقرير
The Spherical Hecke algebra, partition functions, and motivic integration
| العنوان: | The Spherical Hecke algebra, partition functions, and motivic integration |
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| المؤلفون: | Casselman, William, Cely, Jorge E., Hales, Thomas |
| سنة النشر: | 2016 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, Mathematics - Number Theory |
| الوصف: | 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). Comment: 45 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1611.05773 |
| رقم الأكسشن: | edsarx.1611.05773 |
| قاعدة البيانات: | arXiv |
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