Quantizations of nilpotent orbits vs 1-dimensional representations of W-algebras

摘要: Let g be a semisimple Lie algebra over an algebraically closed field K of characteristic 0 and O nilpotent orbit in g. Then Orb is symplectic algebraic variety one can ask whether it possible to quantize $\Orb$ (in appropriate sense) and, if so, how classify the quantizations. On other hand, for pair (g,O) construct associative W called (finite) W-algebra. The goal this paper clarify relationship between quantizations (and its coverings) 1-dimensional W-modules. In first approximation, our result that there one-to-one correspondence two. not new: was discovered different form) by Moeglin 80's.