We extend our investigations on $\mathfrak g$-invariant Fedosov star products
and quantum momentum mappings \cite{MN03a} to star products of Wick type on
pseudo-K\"ahler manifolds. Star products of Wick type can be completely
characterized by a local description as given by Karabegov in \cite{Kar96} for
star products with separation of variables. We separately treat the action of a
Lie group $G$ on $\Cinf{M}[[\nu]]$ by (pull-backs with) diffeomorphisms and the
action of a Lie algebra $\mathfrak g$ on $\Cinf{M}[[\nu]]$ by (Lie derivatives
with respect to) vector fields. Within Karabegov's framework we prove necessary
and sufficient conditions for a given star product of Wick type to be invariant
in the respective sense. Moreover, our results yield a complete classification
of invariant star products of Wick type. We also prove a necessary and
sufficient condition for (the Lie derivative with respect to) a vector field to
be even a quasi-inner derivation of a given star product of Wick type. We then
transfer our former results about quantum momentum mappings for $\mathfrak
g$-invariant Fedosov star products to the case of invariant star products of
Wick type.
@article{0307324,
author = {Mueller-Bahns, Michael F. and Neumaier, Nikolai},
title = {Invariant Star Products of Wick Type: Classification and Quantum
Momentum Mappings},
journal = {arXiv},
volume = {2003},
number = {0},
year = {2003},
language = {en},
url = {http://dml.mathdoc.fr/item/0307324}
}
Mueller-Bahns, Michael F.; Neumaier, Nikolai. Invariant Star Products of Wick Type: Classification and Quantum
Momentum Mappings. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0307324/