Strict Quantization for Compact Pseudo-K\"ahler Manifolds and Group Actions
Symplectic Geometry
2025-06-26 v2
Abstract
The asymptotic results for Berezin-Toeplitz operators yield a strict quantization for the algebra of smooth functions on a given Hodge manifold. It seems natural to generalize this picture for quantizable pseudo-K\"ahler manifolds in presence of a group action. Thus, in this setting we introduce a Berezin transform which has a complete asymptotic expansion on the preimage of the zero set of the moment map. It leads in a natural way to prove that certain quantization maps are strict.
Cite
@article{arxiv.2410.03322,
title = {Strict Quantization for Compact Pseudo-K\"ahler Manifolds and Group Actions},
author = {Andrea Galasso},
journal= {arXiv preprint arXiv:2410.03322},
year = {2025}
}