Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions

Andrea Galasso

Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca, Via R. Cozzi 55, 20125 Milano, Italy

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-Kähler 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.

Keywords: CR manifolds, Toeplitz operators, star products, group actions.

MSC: 32V20, 32A25, 53D50

Received: January 29, 2025; in final form June 17, 2025; Published online June 25, 2025

Language: English

DOI: 10.3842/SIGMA.2025.048

ArXiv: 2410.03322