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Alexander Alldridge

  1. Integration on Non-Compact Supermanifolds.

    Пнд, 06/13/2011 - 15:01 — SomNambul
    Authors: Alexander Alldridge, Joachim Hilgert, Wolfgang Palzer
    Subjects: Differential Geometry
    Abstract

    We investigate the Berezin integral of non-compactly supported quantities. In
    the framework of supermanifolds with corners, we give a general, explicit and
    coordinate-free repesentation of the boundary terms introduced by an arbitrary
    change of variables. As a corollary, a general Stokes's theorem is derived -
    here, the boundary integral contains transversal derivatives of arbitrarily
    high order.

  2. The Harish-Chandra isomorphism for reductive symmetric superpairs.

    Ср, 04/07/2010 - 15:01 — SomNambul
    Authors: Alexander Alldridge
    Subjects: Representation Theory
    Abstract

    For a symmetric pair of Lie superalgebras which is strongly reductive and of
    even type, we introduce the graded Harish-Chandra homomorphism and,
    generalising results of Harish-Chandra, V. Kac, and M. Gorelik, show that its
    image coincides with the image of Chevalley's restriction map on symmetric
    invariants. The latter is known by the graded generalisation of Chevalley's
    restriction theorem that we have obtained jointly with J. Hilgert and M.R.
    Zirnbauer.

  3. Invariant Berezin integration on homogeneous supermanifolds.

    Ср, 11/18/2009 - 16:01 — SomNambul
    Authors: Alexander Alldridge, Joachim Hilgert
    Subjects: Differential Geometry
    Abstract

    Let G be a Lie supergroup and H a closed subsupergroup. We study the
    unimodularity of the homogeneous supermanifold G/H, i.e. the existence of
    G-invariant sections of its Berezinian line bundle. To that end, we express
    this line bundle as a G-equivariant associated bundle of the principal H-bundle
    G over G/H. We also study the fibre integration of Berezinians on oriented
    fibre bundles. As an application, we prove a formula of `Fubini' type: the
    invariant integral over G can be expressed (up to sign) by a succesive
    invariant integration over H and G/H.

  4. Chevalley's restriction theorem for reductive symmetric superpairs.

    Пт, 11/06/2009 - 16:01 — SomNambul
    Authors: Alexander Alldridge, Joachim Hilgert, Martin R. Zirnbauer
    Subjects: Representation Theory
    Abstract

    Let (g,k) be a reductive symmetric superpair of even type, i.e. so that there
    exists an even Cartan subspace a in p. The restriction map S(p^*)^k->S(a^*)^W
    where W=W(g_0:a) is the Weyl group, is injective. We determine its image
    explicitly.

  5. Infinite-dimensional supermanifolds over arbitrary base fields.

    Чт, 10/29/2009 - 16:01 — SomNambul
    Authors: Alexander Alldridge, Martin Laubinger
    Subjects: Differential Geometry
    Abstract

    In his recent investigation of a super Teichmueller space, Sachse (2007),
    based on work of Molotkov (1984), has proposed a theory of Banach
    supermanifolds in the framework of functor categories (i.e. using the 'functor
    of points' approach of Bernstein and Schwarz). Using the differential calculus
    of Bertram-Glockner-Neeb (2004), we extend Sachse's approach to supermanifolds
    modeled over arbitrary Hausdorff topological super-vector spaces over an
    arbitrary non-discrete Hausdorff topological field of characteristic zero.

  6. Boundary orbit strata and faces of invariant cones and complex Olshanskii semigroups.

    Втр, 08/25/2009 - 22:41 — SomNambul
    Authors: Alexander Alldridge
    Subjects: Complex Variables
    Abstract

    Let D=G/K be an irreducible Hermitian symmetric domain. Then G is contained
    in a complexification, and there exists a closed complex subsemigroup, the
    so-called minimal Olshanskii semigroup, of the complexification characterised
    by the fact that all holomorphic discrete series representations of G extend
    holomorphically to it. Parallel to the classical theory of boundary strata for
    the symmetric domain D, due to Koranyi and Wolf, we give a detailed and
    complete description of the K-orbit type strata of the minimal Olshanskii
    semigroup, as K-equivariant fibre bundles.

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