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Highlights in Lie Algebraic Methods pp 167–188Cite as

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Weyl Denominator Identity for Finite-Dimensional Lie Superalgebras

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Part of the book series: Progress in Mathematics ((PM,volume 295))

Abstract

Weyl denominator identity for the basic simple Lie superalgebras was formulated by Kac and Wakimoto and was proven by them for the defect one case. In this paper we prove the identity for the rest of the cases.

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References

  1. M. Gorelik, Weyl denominator identity for affine Lie superalgebras with non-zero dual Coxeter number, J. Algebra, 337 (2011), 50–62.

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  2. A. Joseph, Quantum groups and their primitive ideals, Erdebnisse der Mathematik und ihrer Grenzgebiete 3, 29, Springer, Berlin, 1995.

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  6. V. G. Kac, M. Wakimoto, Integrable highest weight modules over affine superalgebras and number theory, in Lie Theory and Geometry, 415–456, Progress in Math., 123, Birkhäuser, Boston, 1994.

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  7. V. Serganova, Kac–Moody superalgebras and integrability. Developments and trends in infite-dimensional Lie theory, 169–218, Progr. Math., 288, Birkhäuser, Boston, MA, 2011.

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Acknowledgements

I am very grateful to V. Kac for his patience and useful comments. I would like to thank D. Novikov and A. Novikov for their support. Supported in part by ISF Grant No. 1142/07 and by the Minerva foundation with funding from the Federal German Ministry for Education and Research.

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Authors and Affiliations

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

    Maria Gorelik

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  1. Maria Gorelik
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Correspondence to Maria Gorelik .

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Editors and Affiliations

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

    Anthony Joseph

  2. Department of Mathematics, Univeristy of Haifa, Haifa, 31905, Israel

    Anna Melnikov

  3. School of Engineering and Science, Jacobs University, Bremen, 28759, Germany

    Ivan Penkov

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Gorelik, M. (2012). Weyl Denominator Identity for Finite-Dimensional Lie Superalgebras. In: Joseph, A., Melnikov, A., Penkov, I. (eds) Highlights in Lie Algebraic Methods. Progress in Mathematics, vol 295. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8274-3_7

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