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Supersymmetry in Mathematics and Physics pp 195–239Cite as

Lie Supergroups, Unitary Representations, and Invariant Cones

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2027))

Abstract

The goal of this article is twofold. First, it presents an application of the theory of invariant convex cones of Lie algebras to the study of unitary representations of Lie supergroups. Second, it provides an exposition of recent results of the second author on the classification of irreducible unitary representations of nilpotent Lie supergroups using the method of orbits.

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Acknowledgements

K.-H. Neeb was supported by DFG-grant NE 413/7-1, Schwerpunktprogramm “Darstellungstheorie.” H. Salmasian was supported by an NSERC Discovery Grant and an Alexander von Humboldt Fellowship for Experienced Researchers.

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Authors and Affiliations

  1. Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Bismarckstraße 1½, 91054, Erlangen, Germany

    Karl-Hermann Neeb

  2. Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave., Ottawa, ON, Canada, K1N 6N5

    Hadi Salmasian

Authors
  1. Karl-Hermann Neeb
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  2. Hadi Salmasian
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Correspondence to Hadi Salmasian .

Editor information

Editors and Affiliations

  1. Dépt. Physique, Div. Théorie, CERN, Genève, 1211, Switzerland

    Sergio Ferrara

  2. Department of Mathematics, University of Bologna, Piazza Porta San Donato 5, Bologna, 40126, Italy

    Rita Fioresi

  3. Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, 90095, California, USA

    V.S. Varadarajan

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Neeb, KH., Salmasian, H. (2011). Lie Supergroups, Unitary Representations, and Invariant Cones. In: Ferrara, S., Fioresi, R., Varadarajan, V. (eds) Supersymmetry in Mathematics and Physics. Lecture Notes in Mathematics(), vol 2027. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21744-9_10

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