scholarly journals Coadjoint orbits, moment polytopes, and the Hilbert-Mumford criterion

2000 ◽  
Vol 13 (2) ◽  
pp. 433-466 ◽  
Author(s):  
Arkady Berenstein ◽  
Reyer Sjamaar
Keyword(s):  
Coadjoint Orbits ◽  
Moment Polytopes

scholarly journals Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Fridrich Valach ◽  
Donald R. Youmans
Keyword(s):  
Quantum Mechanics ◽  
Partition Function ◽  
Gauge Group ◽  
Path Integral ◽  
Coadjoint Orbits ◽  
Two Dimensional ◽  
Edge States ◽  
Class Constraint ◽  
Action Functional ◽  
Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

The Darboux coordinate system and Holstein–Primakoff representations on Kähler manifolds

2006 ◽  
Vol 84 (10) ◽  
pp. 891-904
Author(s):  
J R Schmidt
Keyword(s):  
Coordinate System ◽  
Lie Groups ◽  
Lie Algebra ◽  
Poisson Structure ◽  
Kähler Manifolds ◽  
Coadjoint Orbits ◽  
Kahler Manifolds ◽  
Canonical Transformations ◽  
Kahler Geometry

The Kahler geometry of minimal coadjoint orbits of classical Lie groups is exploited to construct Darboux coordinates, a symplectic two-form and a Lie–Poisson structure on the dual of the Lie algebra. Canonical transformations cast the generators of the dual into Dyson or Holstein–Primakoff representations.PACS Nos.: 02.20.Sv, 02.30.Ik, 02.40.Tt

scholarly journals On the Coadjoint Orbits of the Unitriangular Group

1996 ◽  
Vol 180 (2) ◽  
pp. 587-630 ◽  
Author(s):  
Carlos A.M. André
Keyword(s):  
Coadjoint Orbits ◽  
Unitriangular Group

scholarly journals Characters, coadjoint orbits and Duistermaat-Heckman integrals

2021 ◽  
Vol 170 ◽  
pp. 104386
Author(s):  
Anton Alekseev ◽  
Samson L. Shatashvili
Keyword(s):  
Coadjoint Orbits

scholarly journals ADMISSIBLE COADJOINT ORBITS FOR COMPACT LIE GROUPS

2017 ◽  
Vol 23 (3) ◽  
pp. 875-892 ◽  
Author(s):  
P.-E. PARADAN ◽  
M. VERGNE
Keyword(s):  
Lie Groups ◽  
Coadjoint Orbits ◽  
Compact Lie Groups

scholarly journals A Trace Formula for the Quantization of Coadjoint Orbits

2015 ◽  
Vol 2015 (21) ◽  
pp. 11236-11252
Author(s):  
Damien Calaque ◽  
Florian Naef
Keyword(s):  
Trace Formula ◽  
Coadjoint Orbits
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