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• W2556685655 abstract "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)." @default.
• W2556685655 created "2016-11-30" @default.
• W2556685655 creator A5055207622 @default.
• W2556685655 creator A5083681315 @default.
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• W2556685655 date "2016-11-17" @default.
• W2556685655 modified "2023-09-27" @default.
• W2556685655 title "The Spherical Hecke algebra, partition functions, and motivic integration" @default.
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• W2556685655 hasPublicationYear "2016" @default.
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