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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

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Volume 2016, Issue 720


Dirac cohomology and geometric quantization

Meng-Kiat Chuah / Jing-Song Huang
  • Department of Mathematics, Hong Kong University of Science and Technology,Clear Water Bay, Kowloon, Hong Kong SAR, China
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Published Online: 2014-07-09 | DOI: https://doi.org/10.1515/crelle-2014-0050


Let G be a connected real semisimple Lie group having a finite center and a compact Cartan subgroup T with Lie algebra 𝔱0. Let ω be a G×T-invariant symplectic form on X=G×𝔱0. We incorporate Dirac cohomology into the geometric quantization of (X,ω) and study the resulting multiplicity-free unitary G×T-representation on a Hilbert space (X,ω). We also perform symplectic reduction of (X,ω) and show that our quantization method satisfies the principle “quantization commutes with reduction”. As an application we construct various models of discrete series.


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About the article

Received: 2012-12-03

Revised: 2014-04-18

Published Online: 2014-07-09

Published in Print: 2016-11-01

The first named author is supported by a research grant from the Ministry of Science and Technology of Taiwan. The second named author is supported by research grants from the Research Grant Council of Hong Kong SAR and the National Science Foundation of China.

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2016, Issue 720, Pages 33–50, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2014-0050.

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