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Raf Cluckers

  1. Definability results for invariant distributions on a reductive unramified p-adic group.

    Чт, 12/01/2011 - 15:01 — SomNambul
    Authors: Raf Cluckers, Julia Gordon, Immanuel Halupczok
    Subjects: Representation Theory
    Abstract

    Let $G$ be a connected reductive algebraic group over a non-Archimedean local
    field $K$, and let $\mathfrak g$ be its Lie algebra. By a theorem of
    Harish-Chandra, if $K$ has characteristic zero, the Fourier transforms of
    nilpotent orbital integrals are represented on the set of regular elements in
    ${\mathfrak g}(K)$ by locally constant functions, which, extended by zero to
    all of ${\mathfrak g}(K)$, are locally integrable. In this paper, we prove that
    if the group $G$ is unramified, these functions are in fact specializations of
    constructible motivic exponential functions.

  2. On the computability of some positive-depth supercuspidal characters near the identity.

    Пнд, 02/01/2010 - 16:01 — SomNambul
    Authors: Raf Cluckers, Clifton Cunningham, Julia Gordon, Loren Spice
    Subjects: Representation Theory
    Abstract

    This paper is concerned with the values of Harish-Chandra characters of a
    class of positive-depth, toral, very supercuspidal representations of $p$-adic
    symplectic and special orthogonal groups, near the identity element. We declare
    two representations equivalent if their characters coincide on a specific
    neighbourhood of the identity (which is larger than the neighbourhood on which
    Harish-Chandra local character expansion holds).

  3. Analytic van der Corput Lemma for p-adic and F_q((t)) oscillatory integrals, singular Fourier transforms, and restriction theorems.

    Чт, 01/14/2010 - 16:01 — SomNambul
    Authors: Raf Cluckers
    Subjects: Functional Analysis
    Abstract

    We give the p-adic and F_q((t)) analogue of the real van der Corput Lemma,
    where the real condition of sufficient smoothness for the phase is replaced by
    the condition that the phase is a convergent power series. This van der Corput
    style result allows us, in analogy to the real situation, to study singular
    Fourier transforms on suitably curved (analytic) manifolds and opens the way
    for further applications.

  4. Stability under integration of sums of products of real globally subanalytic functions and their logarithms.

    Втр, 11/24/2009 - 16:01 — SomNambul
    Authors: Raf Cluckers, Daniel J. Miller
    Subjects: Algebraic Geometry
    Abstract

    We study Lebesgue integration of sums of products of globally subanalytic
    functions and their logarithms, called constructible functions. Our first
    theorem states that the class of constructible functions is stable under
    integration. The second theorem treats integrability conditions in Fubini-type
    settings, and the third result gives decay rates at infinity for constructible
    functions. Further, we give preparation results for constructible functions
    related to integrability conditions.

  5. Fields with Analytic Structure.

    Втр, 08/18/2009 - 11:53 — SomNambul
    Authors: Raf Cluckers, Leonard Lipshitz
    Subjects: Logic
    Abstract

    We present a unifying theory of fields with certain classes of analytic
    functions, called fields with analytic structure. Both real closed fields and
    Henselian valued fields are considered.

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