QUANTUM MOMENT MAPS AND INVARIANTS FOR G-INVARIANT STAR PRODUCTS

Abstract

We study a quantum moment map and propose an invariant for G-invariant star products on a G-transitive symplectic manifold. We start by describing a new method to construct a quantum moment map for G-invariant star products of Fedosov type. We use it to obtain an invariant that is invariant under G-equivalence. In the last section we give two simple examples of such invariants, which involve non-classical terms and provide new insights into the classification of G-invariant star products.