Virasoro Coadjoint Orbits

2017 ◽  
pp. 201-240
Author(s):  
Blagoje Oblak
Keyword(s):  
Coadjoint Orbits

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

scholarly journals Superunitary Representations of Heisenberg Supergroups

2018 ◽  
Vol 2020 (19) ◽  
pp. 5926-6006 ◽  
Author(s):  
Axel de Goursac ◽  
Jean-Philippe Michel
Keyword(s):  
Representation Theory ◽  
Heisenberg Group ◽  
Fourier Transformation ◽  
Coadjoint Orbits ◽  
New Approach ◽  
Von Neumann ◽  
Neumann Theorem ◽  
Lie Supergroups ◽  
Definition Of ◽  
Von Neumann Theorem

Abstract Numerous Lie supergroups do not admit superunitary representations (SURs) except the trivial one, for example, Heisenberg and orthosymplectic supergroups in mixed signature. To avoid this situation, we introduce in this paper a broader definition of SUR, relying on a new definition of Hilbert superspace. The latter is inspired by the notion of Krein space and was developed initially for noncommutative supergeometry. For Heisenberg supergroups, this new approach yields a smooth generalization, whatever the signature, of the unitary representation theory of the classical Heisenberg group. First, we obtain Schrödinger-like representations by quantizing generic coadjoint orbits. They satisfy the new definition of irreducible SURs and serve as ground to the main result of this paper: a generalized Stone–von Neumann theorem. Then, we obtain the superunitary dual and build a group Fourier transformation, satisfying Parseval theorem. We eventually show that metaplectic representations, which extend Schrödinger-like representations to metaplectic supergroups, also fit into this definition of SURs.

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