Work

Quantization and reduction for torsion free CR manifolds

Year: 2025

Type: article

Abstract: Consider a compact torsion free CR manifold $X$ and assume that $X$ admits a compact CR Lie group action $G$. Let $L$ be a $G$-equivariant rigid CR line bundle over $X$. It seems natural to consider the space of $G$-invariant CR sections in the high tensor powers as quantization space, on which a certain weighted $G$-invariant Fourier-Szegő operator projects. Under certain natural assumptions, we show that the group invariant Fourier-Szegő projector admits a full asymptotic expansion. As an application, if the tensor power of the line bundle is large enough, we prove that quantization commutes with reduction.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2025.111225

Authors: Andrea Galasso, Chin-Yu Hsiao

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Università degli Studi di Milano-Bicocca, Ministry of Science and Technology, Taiwan, Universität zu Köln

Awards: G5107450183, G616776308