Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions

2024/10/04 by Galasso, Andrea
#FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2410.03322

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.

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