Differentiability of quantum moment maps and G - invariant star products

Abstract

We study quantum moment maps of G-invariant star products, a quantum analogue of the moment map for classical Hamiltonian systems. Introducing an integral representation, we show that any quantum moment map for a G-invariant star product is differentiable. This property gives us a new method for the classification of G-invariant star products on regular coadjoint orbits of compact semisimple Lie groups.