Joachim Hilgert
Integration on Non-Compact Supermanifolds.
Mon, 06/13/2011 - 15:01 — SomNambulAuthors: Alexander Alldridge, Joachim Hilgert, Wolfgang Palzer
Subjects: Differential Geometry
AbstractWe 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.Invariant Berezin integration on homogeneous supermanifolds.
Wed, 11/18/2009 - 16:01 — SomNambulAuthors: Alexander Alldridge, Joachim Hilgert
Subjects: Differential Geometry
AbstractLet 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.Chevalley's restriction theorem for reductive symmetric superpairs.
Fri, 11/06/2009 - 16:01 — SomNambulAuthors: Alexander Alldridge, Joachim Hilgert, Martin R. Zirnbauer
Subjects: Representation Theory
AbstractLet (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.Patterson--Sullivan distributions for rank one symmetric spaces of the noncompact type.
Mon, 09/14/2009 - 09:01 — SomNambulAuthors: Joachim Hilgert, Michael Schroeder
Subjects: Spectral Theory
AbstractThere is a remarkable relation between two kinds of phase space distributions
associated to eigenfunctions of the Laplacian of a compact hyperbolic manifold:
It was observed in \cite{AZ} that for compact hyperbolic surfaces
$X_{\Gamma}=\Gamma\backslash\mathbb{H}$ Wigner distributions $\int_{S^*
X_{\Gamma}} a dW_{ir_j} = < Op(a)\phi_{ir_j},\phi_{ir_j}>_{L^2(X_{\Gamma})}$
and Patterson--Sullivan distributions $PS_{ir_j}$ are asymptotically equivalent
as $r_j\to\infty$.
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