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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1994 Jun 21;91(13):6026–6029. doi: 10.1073/pnas.91.13.6026

Minimal representations, geometric quantization, and unitarity.

R Brylinski 1, B Kostant 1
PMCID: PMC44130  PMID: 11607478

Abstract

In the framework of geometric quantization we explicitly construct, in a uniform fashion, a unitary minimal representation pio of every simply-connected real Lie group Go such that the maximal compact subgroup of Go has finite center and Go admits some minimal representation. We obtain algebraic and analytic results about pio. We give several results on the algebraic and symplectic geometry of the minimal nilpotent orbits and then "quantize" these results to obtain the corresponding representations. We assume (Lie Go)C is simple.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Brylinski R., Kostant B. Minimal representations of E6, E7, and E8 and the generalized Capelli identity. Proc Natl Acad Sci U S A. 1994 Mar 29;91(7):2469–2472. doi: 10.1073/pnas.91.7.2469. [DOI] [PMC free article] [PubMed] [Google Scholar]

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