Sur les ℓ-blocs de niveau zéro des groupes p-adiques II

2018/06/25 by Lanard, Thomas
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1806.09543

Abstract

Let G be a p-adic group which splits over an unramified extension and Rep_Λ⁰(G) the abelian category of smooth level 0 representations of G with coefficients in Λ=ℚ_ℓ or ℤ_ℓ. We study the finest decomposition of Rep_Λ⁰(G) into a product of subcategories that can be obtained by the method introduced in an article of Lanard (arXiv:1703.08689), which is currently the only one available when Λ=ℤ_ℓ and G is not an inner form of GL_n. We give two descriptions of it, a first one on the group side à la Deligne-Lusztig, and a second one on the dual side à la Langlands. We prove several fundamental properties, like for example the compatibility with parabolic induction and restriction or the compatibility with the local Langlands correspondence. The factors of this decomposition are not blocks, but we show how to group them to obtain "stable" blocks.

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