Boundedness for Weyl–Pedersen Calculus on Flat Coadjoint Orbits

Quantization of Nilpotent Coadjoint Orbits Quantization of Nilpotent Coadjoint Orbits Quantization of Nilpotent Coadjoint Orbits

Let G be a complex reductive group. We study the problem of associating Dixmier algebras to nilpotent (co)adjoint orbits of G, or, more generally, to orbit data for G. If g = 0 + n + in is a triangular decomposition of g and 0 is a nilpotent orbit, we consider the irreducible components of 0 n n, which are Lagrangian subvarieties of 0. The main idea is to construct, starting with certain "good"...

Star Products on Coadjoint Orbits

Compact Coadjoint Orbits

I give an answer to the question “Which groups have compact coadjoint orbits?”. Whilst I thought that the answer, which is straightforward, must be in the literature, I was unable to find it. This note aims to rectify this. It is also a plea: If the result is already published then I would like to be told the reference.

Holstein-Primakoff Realizations on Coadjoint Orbits

We derive the Holstein-Primakoff oscillator realization on the coadjoint orbits of the SU(N + 1) and SU(1, N) group by treating the coadjoint orbits as a constrained system and performing the symplectic reduction. By using the action-angle variables transformations, we transform the original variables into Darboux variables. The Holstein-Primakoff expressions emerge after quantization in a cano...

Magnetic Geodesic Flows on Coadjoint Orbits

We describe a class of completely integrable G-invariant magnetic geodesic flows on (co)adjoint orbits of a compact connected Lie group G with magnetic field given by the Kirillov-Konstant 2-form.