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- W4287777663 abstract "Let G be a reductive p-adic group and let Rep(G)^s be a Bernstein block in the category of smooth complex G-representations. We investigate the structure of Rep(G)^s, by analysing the algebra of G-endomorphisms of a progenerator Pi of that category. We show that Rep(G)^s is almost Morita equivalent with a (twisted) affine Hecke algebra. This statement is made precise in several ways, most importantly with a family of (twisted) graded algebras. It entails that, as far as finite length representations are concerned, Rep(G)^s and End_G (Pi)-Mod can be treated as the module category of a twisted affine Hecke algebra. We draw two consequences. Firstly, we show that the equivalence of categories between Rep(G)^s and End_G (Pi)-Mod preserves temperedness of finite length representations. Secondly, we provide a classification of the irreducible representations in Rep(G)^s, in terms of the complex torus and the finite group canonically associated to Rep(G)^s. This proves a version of the ABPS conjecture and enables us to express the set of irreducible $G$-representations in terms of the supercuspidal representations of the Levi subgroups of $G$. Our methods are independent of the existence of types, and apply in complete generality." @default.
- W4287777663 created "2022-07-26" @default.
- W4287777663 creator A5037088750 @default.
- W4287777663 date "2020-05-16" @default.
- W4287777663 modified "2023-09-23" @default.
- W4287777663 title "Endomorphism algebras and Hecke algebras for reductive p-adic groups" @default.
- W4287777663 doi "https://doi.org/10.48550/arxiv.2005.07899" @default.
- W4287777663 hasPublicationYear "2020" @default.
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