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Representations of Lie Superalgebras

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Perspectives in Lie Theory

Part of the book series: Springer INdAM Series ((SINDAMS,volume 19))

Abstract

Abstract In these notes we give an introduction to representation theory of simple finite-dimensional Lie superalgebras. We concentrate on so called basic superalgebras. Those are superalgebras which have even reductive part and admit an invariant form. We start with structure theory of basic superalgebras emphasizing abstract properties of roots and then proceed to representations, trying to demonstrate the variety of methods: Harish-Chandra homomorphism, support variety, translation functors, Borel-Weil-Bott theory and localization.

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Notes

  1. 1.

    A grading is compatible if and .

  2. 2.

    This assumption is not essential and can be dropped. It is here only for convenience of notations.

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Acknowledgements

I thank the organizers of the workshop in Pisa for giving me the opportunity to give this minicourse and Rita Fioresi for writing the lecture notes. I thank the referee for pointing out numerous missprints in the first version of the paper. I also acknowledge partial support of NSF grant DMS-1303301.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, 970 Evans Hall 3840, Berkeley, CA, 94720–3840, USA

    Vera Serganova

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  1. Vera Serganova
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Correspondence to Vera Serganova .

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Editors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    Filippo Callegaro

  2. Dipartimento di Matematica, University of Padova, Padova, Italy

    Giovanna Carnovale

  3. Dipartimento di Matematica, University of Bologna, Bologna, Italy

    Fabrizio Caselli

  4. Dipartimento di Matematica, Sapienza University of Rome, Roma, Italy

    Corrado De Concini

  5. Dipartimento di Matematica, Sapienza University of Rome, Roma, Italy

    Alberto De Sole

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Serganova, V. (2017). Representations of Lie Superalgebras. In: Callegaro, F., Carnovale, G., Caselli, F., De Concini, C., De Sole, A. (eds) Perspectives in Lie Theory. Springer INdAM Series, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-58971-8_3

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