Noncommutative smoothness and 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"...

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.

Coadjoint Orbits, Spin and Dequantization

In this Letter we propose two path integral approaches to describe the classical mechanics of spinning particles. We show how these formulations can be derived from the associated quantum ones via a sort of geometrical dequantization procedure proposed in a previous paper.

Coadjoint Orbits and Induced Representations

Coadjoint orbits of Lie groups play important roles in several areas of mathematics and physics. In particular, in representation theory, Kirillov showed in the 1960's that for nilpotent Lie groups there is a one-one correspondence between coadjoint orbits and irreducible unitary representations. Subsequently this result was extensively generalized by Kostant, Auslander-Kostant, Duflo, Vogan an...

Star Products on Coadjoint Orbits