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arXiv · 2410.03322

Strict Quantization for Compact Pseudo-K\"ahler Manifolds and Group Actions

Andrea Galasso
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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.

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Andrea Galasso. 2024-10-04. Strict Quantization for Compact Pseudo-K\"ahler Manifolds and Group Actions. https://doi.org/10.3842/sigma.2025.048

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