A classification of irreducible admissible mod p representations of p-adic reductive groups

Abstract

Let F be a locally compact non-archimedean field, p its residue characteristic, and G a connected reductive group over F. Let C an algebraically closed field of characteristic p. We give a complete classification of irreducible admissible C-representations of G = G(F), in terms of supercuspidal C-representations of the Levi subgroups of G, and parabolic induction. Thus we push to their natural conclusion the ideas of the third-named author, who treated the case G = GL_m, as further expanded by the first-named author, who treated split groups G. As in the split case, we first get a classification in terms of supersingular representations of Levi subgroups, and as a consequence show that supersingularity is the same as supercuspidality.

64 pages

References in corpus (1)

• On special representations of $p$-adic reductive groups

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• On the exactness of ordinary parts over a local field of characteristic $p$
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• A comparison between pro-$p$ Iwahori-Hecke modules and mod $p$ representations
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• Deformation rings and parabolic induction
• Geometrization of the Satake transform for mod $p$ Hecke algebras
• Restriction of $p$-modular representations of $U(2,1)$ to a Borel subgroup
• From $p$-modular to $p$-adic Langlands correspondences for $U(1,1)({\mathbb{Q}}_{p^2}/{\mathbb{Q}}_p)$: deformations in the non-supercuspidal case