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• W3136244411 abstract "Let G be a reductive group over a non-archimedean local field F. Consider an arbitrary Bernstein block Rep(G)^s in the category of complex smooth G-representations. In earlier work the author showed that there exists an affine Hecke algebra H(O,G) whose category of right modules is closely related to Rep(G)^s. In many cases this is in fact an equivalence of categories, like for Iwahori-spherical representations. In this paper we study the q-parameters of the affine Hecke algebras H(O,G). We compute them in many cases, in particular for principal series representations of quasi-split groups and for classical groups. Lusztig conjectured that the q-parameters are always integral powers of q_F and that they coincide with the q-parameters coming from some Bernstein block of unipotent representations. We reduce this conjecture to the case of simple p-adic groups, and we prove it for most of those." @default.
• W3136244411 created "2021-03-29" @default.
• W3136244411 creator A5037088750 @default.
• W3136244411 date "2021-03-24" @default.
• W3136244411 modified "2023-09-27" @default.
• W3136244411 title "Parameters of Hecke algebras for Bernstein components of p-adic groups" @default.
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