Deformation Quantization of non Regular Orbits of Compact Lie Groups

A Review on Deformation Quantization of Coadjoint Orbits of Semisimple Lie Groups

In this paper we make a review of the results obtained in previous works by the authors on deformation quantization of coadjoint orbits of semisimple Lie groups. We motivate the problem with a new point of view of the well known Moyal-Weyl deformation quantization. We consider only semisimple orbits. Algebraic and differential deformations are compared. Investigation supported by the University...

Deformation Quantization of Coadjoint Orbits

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. Let G be a complex Lie group of dimension n and GR a real form of G. Let G and GR be their respective Lie algebras with Lie bracket [ , ]. As it is well known, ...

Algebraic and Differential Star Products on Regular Orbits of Compact Lie Groups

Quantum Co-adjoint Orbits of the Real Diamond Group

We present explicit formulas for deformation quantization on the coadjoint orbits of the real diamond Lie group. From this we obtain quantum halfplans, quantum hyperbolic cylinders, quantum hyperbolic paraboloids via Fedosov deformation quantization and finally, the corresponding unitary representations of this group.

Geometric Quantization of Real Minimal Nilpotent Orbits

In this paper, we begin a quantization program for nilpotent orbits OR of a real semisimple Lie group GR. These orbits arise naturally as the coadjoint orbits of GR which are stable under scaling, and thus they have a canonical symplectic structure ω where the GR-action is Hamiltonian. These orbits and their covers generalize the oscillator phase space T R, which occurs here when GR = Sp(2n,R) ...