Differentiability of quantum moment maps and G - invariant star products

Kentaro Hamachi

Vol. 216 (2004), No. 1, 127–148

DOI: 10.2140/pjm.2004.216.127

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.

Milestones

Received: 27 September 2002

Revised: 8 July 2003

Published: 1 September 2004