Joseph A. Wolf
A duality for the double fibration transform.
Thu, 02/09/2012 - 15:01 — SomNambulAuthors: Joseph A. Wolf, Michael G. Eastwood
Subjects: Representation Theory
AbstractWe establish a duality within the spectral sequence that governs the
holomorphic double fibration transform. It has immediate application to the
questions of injectivity and range characterization for this transform. We
discuss some key examples and an improved duality that holds in the Hermitian
holomorphic case.Pseudo-Riemannian Weakly Symmetric Manifolds.
Tue, 07/26/2011 - 15:01 — SomNambulAuthors: Joseph A. Wolf, Zhiqi Chen
Subjects: Differential Geometry
AbstractThere is a well developed theory of weakly symmetric Riemannian manifolds.
Here it is shown that several results in the Riemannian case are also valid for
weakly symmetric pseudo-Riemannian manifolds, but some require additional
hypotheses. The topics discussed are homogeneity, geodesic completeness, the
geodesic orbit property, weak symmetries, and the structure of the nilradical
of the isometry group.Branching of Representations to Symmetric Subgroups.
Mon, 09/28/2009 - 15:24 — SomNambulAuthors: Joseph A. Wolf, Michael G. Eastwood
Subjects: Representation Theory
AbstractLet $\gg$ be the Lie algebra of a compact Lie group and let $\theta$ be any
automorphism of $\gg$. Let $\gk$ denote the fixed point subalgebra
$\gg^\theta$. In this paper we present LiE programs that, for any finite
dimensional complex representation $\pi$ of $\gg$, give the explicit branching
$\pi|_\gk$ of $\pi$ on $\gk$.Infinite Dimensional Multiplicity Free Spaces III: Matrix Coefficients and Regular Functions.
Thu, 09/10/2009 - 10:12 — SomNambulAuthors: Joseph A. Wolf
Subjects: Representation Theory
AbstractIn earlier papers we studied direct limits $(G,K) = \varinjlim (G_n,K_n)$ of
two types of Gelfand pairs. The first type was that in which the $G_n/K_n$ are
compact Riemannian symmetric spaces. The second type was that in which $G_n =
N_n\rtimes K_n$ with $N_n$ nilpotent, in other words pairs $(G_n,K_n)$ for
which $G_n/K_n$ is a commutative nilmanifold.Infinite Dimensional Multiplicity Free Spaces III: Matrix Coefficients and Regular Functions.
Thu, 09/10/2009 - 10:12 — SomNambulAuthors: Joseph A. Wolf
Subjects: Representation Theory
AbstractIn earlier papers we studied direct limits $(G,K) = \varinjlim (G_n,K_n)$ of
two types of Gelfand pairs. The first type was that in which the $G_n/K_n$ are
compact Riemannian symmetric spaces. The second type was that in which $G_n =
N_n\rtimes K_n$ with $N_n$ nilpotent, in other words pairs $(G_n,K_n)$ for
which $G_n/K_n$ is a commutative nilmanifold.
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