scholarly journals Geometric Quantization¶and the Generalized Segal--Bargmann Transform¶for Lie Groups of Compact Type

2002 ◽  
Vol 226 (2) ◽  
pp. 233-268 ◽  
Author(s):  
Brian C. Hall
Keyword(s):  
Lie Groups ◽  
Geometric Quantization ◽  
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.

scholarly journals Fock model and Segal–Bargmann transform for minimal representations of Hermitian Lie groups

2012 ◽  
Vol 263 (11) ◽  
pp. 3492-3563 ◽  
Author(s):  
Joachim Hilgert ◽  
Toshiyuki Kobayashi ◽  
Jan Möllers ◽  
Bent Ørsted
Keyword(s):  
Lie Groups ◽  
Bargmann Transform ◽  
Minimal Representations

scholarly journals Almost paracontact and parahodge structures on manifolds

1985 ◽  
Vol 99 ◽  
pp. 173-187 ◽  
Author(s):  
Soji Kaneyuki ◽  
Floyd L. Williams
Keyword(s):  
Lie Groups ◽  
Geometric Quantization ◽  
Contact Structures ◽  
Simple Lie Groups ◽  
Coset Spaces ◽  
Adjoint Orbits ◽  
Simply Connected

In this paper we study the paracomplex analogues of almost contact structures, and we introduce and study the notion of parahodge structures on manifolds. In particular, we construct new examples of paracomplex manifolds and we find all simply connected parahermitian symmetric coset spaces, which are the adjoint orbits of noncompact simple Lie groups, with parahodge structures induced by the Killing forms. This is done by (i) observing that a version of the results of A. Morimoto [4] on almost contact structures can be formulated and proved for almost paracontact structures, and by (ii) the methods of geometric quantization [3] applied to parahermitian symmetric triples [1] in conjunction with results of [7]. Two of the main results are Theorem 2.5 (which ties together the above structures) and Corollary 3.9.

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