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Florian Herzig

  1. The classification of irreducible admissible mod p representations of a p-adic GL_n.

    Ср, 05/12/2010 - 15:01 — SomNambul
    Authors: Florian Herzig
    Subjects: Number Theory
    Abstract

    Let F be a finite extension of Q_p. Using the mod p Satake transform, we
    define what it means for an irreducible admissible smooth representation of an
    F-split p-adic reductive group over \bar F_p to be supersingular. We then give
    the classification of irreducible admissible smooth GL_n(F)-representations
    over \bar F_p in terms of supersingular representations. As a consequence we
    deduce that supersingular is the same as supercuspidal. These results
    generalise the work of Barthel-Livne for n = 2. For general split reductive
    groups we obtain similar results under stronger hypotheses.

  2. A Satake isomorphism in characteristic p.

    Пнд, 10/26/2009 - 14:11 — SomNambul
    Authors: Florian Herzig
    Subjects: Number Theory
    Abstract

    Suppose that G is a connected reductive group over a p-adic field F, that K
    is a hyperspecial maximal compact subgroup of G(F), and that V is an
    irreducible representation of K over the algebraic closure of the residue field
    of F. We establish an analogue of the Satake isomorphism for the Hecke algebra
    of compactly supported, K-biequivariant functions f: G(F) \to End V. These
    Hecke algebras were first considered by Barthel-Livne for GL_2.

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