scholarly journals DEFORMATION QUANTIZATION OF COADJOINT ORBITS

2000 ◽  
Vol 14 (22n23) ◽  
pp. 2397-2400 ◽  
Author(s):  
M. A. LIEDÓ
Keyword(s):  
Lie Groups ◽  
Algebraic Structure ◽  
Deformation Quantization ◽  
Geometric Quantization ◽  
Coadjoint Orbits ◽  
Semisimple Lie Groups

A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.

scholarly journals Polynomial algebras on coadjoint orbits of semisimple Lie groups

2002 ◽  
Vol 170 (1) ◽  
pp. 29-34
Author(s):  
Mark J. Gotay ◽  
Janusz Grabowski ◽  
Bryon Kaneshige
Keyword(s):  
Lie Groups ◽  
Coadjoint Orbits ◽  
Semisimple Lie Groups ◽  
Polynomial Algebras

scholarly journals Contractions of group representations via geometric quantization

2019 ◽  
Vol 110 (1) ◽  
pp. 43-59
Author(s):  
Rauan Akylzhanov ◽  
Alexis Arnaudon
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
General Framework ◽  
Geometric Quantization ◽  
Coadjoint Orbits ◽  
Sufficient Condition ◽  
Group Representations ◽  
Unitary Dual

AbstractWe propose a general framework to contract unitary dual of Lie groups via holomorphic quantization of their coadjoint orbits, using geometric quantization. The sufficient condition for the contractibility of a representation is expressed via cocycles on coadjoint orbits. This condition is verified explicitly for the contraction of SU$$_2$$2 into $$\mathbb {H}$$H. We construct two types of contractions that can be implemented on every matrix Lie group with diagonal contraction matrix.

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