Work

Limit of geometric quantizations on Kähler manifolds with T‐symmetry

Year: 2024

Type: article

Abstract: A compact Kähler manifold with ‐symmetry admits a natural mixed polarization whose real directions come from the ‐action. In Leung and Wang [Adv. Math. 450 (2024), 109756], we constructed a one‐parameter family of Kähler structures ’s with the same underlying Kähler form and , such that (i) there is a ‐equivariant biholomorphism between and and (ii) Kähler polarizations ’s corresponding to ’s converge to as goes to infinity. In this paper, we study the quantum analog of above results. Assume that is a prequantum line bundle on . Let and be quantum spaces defined using polarizations and , respectively. In particular, . They are both representations of . We show that (i) there is a ‐equivariant isomorphism between and and (ii) for regular ‐weight , corresponding ‐weight spaces ’s converge to as goes to infinity.

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.12642

Authors: Naichung Conan Leung, Dan Wang

Institutions: Chinese University of Hong Kong, University of Lisbon, Instituto Superior Técnico

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Chinese University of Hong Kong

Awards: G4546923286, G6235539821