Oscillator algebras with semi-equicontinuous 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"...

Darboux Coordinates on Coadjoint Orbits of Lie Algebras

The method of constructing spectral Darboux coordinates on finite dimensional coadjoint orbits in duals of loop algebras is applied to the one pole case, where the orbit is identified with a coadjoint orbit in the dual of a finite dimensional Lie algebra. The constructions are carried out explicitly when the Lie algebra is sl(2,R), sl(3,R), and so(3,R), and for rank two orbits in so(n,R). A new...

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.

Star Products on Coadjoint Orbits

Cohomological Splitting of Coadjoint Orbits

The rational cohomology of a coadjoint orbit O is expressed as tensor product of the cohomology of other coadjoint orbits O k , with dim O k < dim O. 1 C-splitting of coadjoint orbits The purpose of this note is to express the rational cohomology of a given coadjoint orbit of a compact Lie group in terms of the cohomology of " smaller " coadjoint orbits. Our result is based upon two facts: The ...