On sums of admissible coadjoint orbits

ADMISSIBLE NILPOTENT COADJOINT ORBITS OF p-ADIC REDUCTIVE LIE GROUPS

The orbit method conjectures a close relationship between the set of irreducible unitary representations of a Lie group G, and admissible coadjoint orbits in the dual of the Lie algebra. We define admissibility for nilpotent coadjoint orbits of p-adic reductive Lie groups, and compute the set of admissible orbits for a range of examples. We find that for unitary, symplectic, orthogonal, general...

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.

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 ...