2010 Fiscal Year Final Research Report
Geometric representation theory of affine Hecke algebras and its neighbourbood
| Project/Area Number |
20740011
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
KATO Syu Kyoto University, 理学研究科, 准教授 (40456760)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 冪零錐 / 局所Langlands / 対応 |
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| Research Abstract |
We applied the framework of the eDL correspondence [1,2] to construct a geometric model of tempered representation of affine Hecke algebras of classical types, which is continuous with respect to the parameter deformation [3]. By putting this technique further, we established an algorithm to compute the discrete series characters of affine Hecke algebras of classical types, which interpolates various parameters and types [5]. As an application, we determined the constant in the formal degree formula of affine Hecke algebra, which was left from the study of Opdam and Solleveld. This finalizes the computation of the Plancherel measure of affine Hecke algebras of classical types. In addiction, modulo the result of Bushnell-Henneirt-Kuszko, our result (is supposed to) completes the computation of the Plancherel measure of p-adic groups of classical types.
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