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The Duflo–Serganova Functor, Vingt Ans Après

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Journal of the Indian Institute of Science Aims and scope

Abstract

We review old and new results concerning the \(DS\) functor and associated varieties for Lie superalgebras. These notions were introduced in the unpublished manuscript (Duflo and Serganova in On associated variety for Lie super-algebras, 2005) by Michel Duflo and the third author. This paper includes the results and proofs of the original manuscript, as well as a survey of more recent results.

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Acknowledgements

We would like to thank Kevin Coulembier, Inna Entova-Aizenbud, Thorsten Heidersdorf, Vladimir Hinich, Victor Kac, Victor Ostrik, Ivan Penkov, Julia Pevtsova, Shifra Reif, and Ilya Zakharevich for helpful comments and suggestions. Needless to say, this paper would not have been possible without the original contribution of Michel Duflo. In addition, we thank the referees for very thorough reviews of an earlier version of this article.

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Authors and Affiliations

  1. Department of Mathematics, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Maria Gorelik

  2. Department of Mathematics, Bar-Ilan University, 52900, Ramat Gan, Israel

    Crystal Hoyt

  3. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Vera Serganova

  4. Department of Mathematics, Ben Gurion University, 8410501, Beer-Sheva, Israel

    Alexander Sherman

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  1. Maria Gorelik
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  2. Crystal Hoyt
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Correspondence to Maria Gorelik.

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Funding

M.G. was supported by ISF Grant 1957/21. C.H. was supported by ISF Grant 1221/17. V.S. was supported by NSF Grant 2001191. A.S. was supported by ISF Grant 711/18 and NSF-BSF Grant 2019694.

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The authors have no conflicts of interest.

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To Michel Duflo, with admiration.

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Gorelik, M., Hoyt, C., Serganova, V. et al. The Duflo–Serganova Functor, Vingt Ans Après. J Indian Inst Sci 102, 961–1000 (2022). https://doi.org/10.1007/s41745-022-00334-9

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  • DOI: https://doi.org/10.1007/s41745-022-00334-9

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