Representations of solvable Lie groups and geometric quantization
type: Item
instance of: scholarly article
title: Representations of solvable Lie groups and geometric quantization
zbMATH Open document ID: 0935.22009
DOI: 10.1142/S0252959999000400
author: Qiang Zhao
author: Li Xiao
published in: Chinese Annals of Mathematics. Series B
publication date: 2000-05-04T00:00:00Z
review text: The paper under review uses the theory of geometric quantization for solvable Lie groups developed by Kostant-Sourian and Auslander-Kostant to quantize the covering spaces of coadjoint orbits of solvable Lie groups. The main theorem is that for each integral coadjoint orbit \(O\) and each element \(\sigma\) in the fundamental group \(\pi_1(O)\) of \(O\), there is a corresponding irreducible unitary representation \(\pi(O,\sigma)\) of \(G\). Furthermore, \(\pi(O_1,\sigma_1)\) and \(\pi(O_1,\sigma_2)\) are equivalent if and only if \(O_1\) and \(O_2\) and \(\sigma_1=\sigma_2\). If \(G\) is of type I then every irreducible unitary representation of \(G\) is equivalent to a \(\pi(O,\sigma)\).
Mathematics Subject Classification ID: 22E25
zbMATH DE Number: 1385322
zbMATH Keywords: geometric quantization
zbMATH Keywords: solvable Lie groups
zbMATH Keywords: coadjoint orbits
zbMATH Keywords: unitary representation
Wikidata QID: Q115245108
reviewed by: Jing-Song Huang
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1385322