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1 June 2021 Equivariant deformation quantization and coadjoint orbit method
Naichung Conan Leung, Shilin Yu
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Duke Math. J. 170(8): 1781-1850 (1 June 2021). DOI: 10.1215/00127094-2020-0066

Abstract

Our goal here is to apply deformation quantization to the study of the coadjoint orbit method in the case of real reductive Lie groups. We first prove some general results on the existence of equivariant deformation quantizations of vector bundles on closed Lagrangian subvarieties, which lie in smooth symplectic varieties with Hamiltonian group actions. Then we apply them to the orbit method and construct nontrivial irreducible Harish-Chandra modules for certain nilpotent coadjoint orbits. Our examples include new geometric construction of representations associated to a large class of nilpotent orbits of real exceptional Lie groups.

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Naichung Conan Leung. Shilin Yu. "Equivariant deformation quantization and coadjoint orbit method." Duke Math. J. 170 (8) 1781 - 1850, 1 June 2021. https://doi.org/10.1215/00127094-2020-0066

Information

Received: 15 October 2018; Revised: 20 September 2020; Published: 1 June 2021
First available in Project Euclid: 27 April 2021

Digital Object Identifier: 10.1215/00127094-2020-0066

Subjects:
Primary: 22E46
Secondary: 53D12, 53D55

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 8 • 1 June 2021
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