The representations of Lie groups and geometric quantizations
type: Item
instance of: scholarly article
title: The representations of Lie groups and geometric quantizations
zbMATH Open document ID: 0951.53055
author: Qiang Zhao
published in: Communications in Mathematical Physics
publication date: 2001-01-02T00:00:00Z
review text: The author constructs a number of representations of Lie groups via geometric quantization of coadjoint orbits. It appears that all representations of compact Lie groups, holomorphic discrete series of representations and spherical representations of reductive Lie groups are constructed by geometric quantizations of elliptic and hyperbolic coadjoint orbits. The author successfully constructs Kählerian polarizations and real polarizations for elliptic and hyperbolic coadjoint orbits, respectively. Two classes of coadjoint orbits are quantized using these polarizations.
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 37N20
zbMATH DE Number: 1214085
zbMATH Keywords: Lie groups
zbMATH Keywords: symplectic manifolds
zbMATH Keywords: geometric quantization
Wikidata QID: Q115388661
MaRDI profile type: Publication
full work available at URL: s002200050352
OpenAlex ID: W1998155220
DOI: 10.1007/S002200050352
description: scientific article; zbMATH DE number 1214085