scholarly journals The Segal–Bargmann Transform on a Symmetric Space of Compact Type

1999 ◽  
Vol 165 (1) ◽  
pp. 44-58 ◽  
Author(s):  
Matthew B. Stenzel
Keyword(s):  
Symmetric Space ◽  
Compact Type ◽  
Bargmann Transform

A New Form of the Segal-Bargmann Transform for Lie Groups of Compact Type

1999 ◽  
Vol 51 (4) ◽  
pp. 816-834 ◽  
Author(s):  
Brian C. Hall
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Joint Work ◽  
Compact Type ◽  
Bargmann Transform ◽  
Infinite Dimensional ◽  
Infinite Dimensional Analysis ◽  
Finite Dimensional ◽  
New Form ◽  
Two Parameter

AbstractI consider a two-parameter family Bs,t of unitary transforms mapping an L2-space over a Lie group of compact type onto a holomorphic L2-space over the complexified group. These were studied using infinite-dimensional analysis in joint work with B. Driver, but are treated here by finite-dimensional means. These transforms interpolate between two previously known transforms, and all should be thought of as generalizations of the classical Segal-Bargmann transform. I consider also the limiting cases s → ∞ and s → t/2.

Brownian Motion on a Symmetric Space of Non-Compact Type: Asymptotic Behaviour in Polar Coordinates

1991 ◽  
Vol 43 (5) ◽  
pp. 1065-1085 ◽  
Author(s):  
J. C. Taylor
Keyword(s):  
Brownian Motion ◽  
Symmetric Space ◽  
Asymptotic Behaviour ◽  
Polar Coordinates ◽  
Skew Product ◽  
Compact Type ◽  
Product Representation

AbstractThe results of Orihara [10] and Malliavin2 [7] on the asymptotic behaviour in polar coordinates of Brownian motion on a symmetric space of non-compact type are obtained by means of a skew product representation on K/M x A+of the Brownian motion on the set of regular points of X. Results of Norris, Rogers, and Williams [9] are interpreted in this context.

scholarly journals The fixed point set of a holomorphic isometry, the intersection of two real forms in a Hermitian symmetric space of compact type and symmetric triads

2015 ◽  
Vol 26 (06) ◽  
pp. 1541005 ◽  
Author(s):  
Osamu Ikawa ◽  
Makiko Sumi Tanaka ◽  
Hiroyuki Tasaki
Keyword(s):  
Fixed Point ◽  
Symmetric Space ◽  
Hermitian Symmetric Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Compact Type ◽  
Fixed Point Set ◽  
Point Set ◽  
Necessary And Sufficient ◽  
Real Forms

We show a necessary and sufficient condition that the fixed point set of a holomorphic isometry and the intersection of two real forms of a Hermitian symmetric space of compact type are discrete and prove that they are antipodal sets in the cases. We also consider some relations between the intersection of two real forms and the fixed point set of a certain holomorphic isometry.

scholarly journals On the least positive eigenvalue of the Laplacian for the compact quotient of a certain Riemannian symmetric space

1980 ◽  
Vol 78 ◽  
pp. 137-152 ◽  
Author(s):  
Hajime Urakawa
Keyword(s):  
Fixed Point ◽  
Euclidean Space ◽  
Symmetric Space ◽  
Lie Group ◽  
Discrete Subgroup ◽  
Riemannian Symmetric Space ◽  
Compact Type ◽  
Identity Component ◽  
Rank One ◽  
Quotient Manifold

Let (, g) be the standard Euclidean space or a Riemannian symmetric space of non-compact type of rank one. Let G be the identity component of the Lie group of all isometries of (, g). Let Γ be a discrete subgroup of G acting fixed point freely on whose quotient manifold MΓ is compact.

scholarly journals Dynamics of the heat semigroup on symmetric spaces

2009 ◽  
Vol 30 (2) ◽  
pp. 457-468 ◽  
Author(s):  
LIZHEN JI ◽  
ANDREAS WEBER
Keyword(s):  
Symmetric Space ◽  
Symmetric Spaces ◽  
Chaotic Behavior ◽  
Heat Semigroup ◽  
Euclidean Spaces ◽  
Compact Type ◽  
Heat Semigroups

AbstractThe aim of this paper is to show that the dynamics of Lp heat semigroups (p>2) on a symmetric space of non-compact type is very different from the dynamics of the Lp heat semigroups if 1<p≤2. To see this, we show that certain shifts of the Lp heat semigroups have a chaotic behavior if p>2, and that such a behavior is not possible in the cases 1<p≤2. These results are compared with the corresponding situation for Euclidean spaces and symmetric spaces of compact type, where such a behavior is not possible.

scholarly journals Equivariant harmonic maps depend real analytically on the representation

2021 ◽  
Author(s):  
Ivo Slegers
Keyword(s):  
Symmetric Space ◽  
Symmetric Spaces ◽  
Harmonic Maps ◽  
Main Tool ◽  
Target Space ◽  
Fixed Target ◽  
Compact Type ◽  
Proper Action ◽  
Real Analytic

AbstractWe consider harmonic maps into symmetric spaces of non-compact type that are equivariant for representations that induce a free and proper action on the symmetric space. We show that under suitable non-degeneracy conditions such equivariant harmonic maps depend in a real analytic fashion on the representation they are associated to. The main tool in the proof is the construction of a family of deformation maps which are used to transform equivariant harmonic maps into maps mapping into a fixed target space so that a real analytic version of the results in [4] can be applied.

Sign in / Sign up

Export Citation Format

Share Document