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Enright functors for Kac-Moody superalgebras

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Abstract

A simple generalization of the Enright functor associated with a non-isotropic simple root of Kac-Moody superalgebras is introduced. Two applications for a Kac-Moody superalgebra without isotropic simple root are given: the uniqueness (up to scalar) of homomorphisms between Verma modules and the Malikov-Feigin-Fuks type singular vector formula. The braid relations of the Enright functors are also discussed.

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Acknowledgements

The authors thank the referee for fruitful suggestions. Y.K. was partly supported by the Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research.

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Authors and Affiliations

  1. Université de Lyon, UMR 5208 CNRS, Université Lyon 1, Institut Camille Jordan, 43 Boulevard du 11 Novembre 1918, 69622, Villeurbanne Cedex, France

    Kenji Iohara

  2. Department of Applied Physics, Faculty of Engineering, University of Fukui, Fukui, 910-8507, Japan

    Yoshiyuki Koga

Authors
  1. Kenji Iohara
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  2. Yoshiyuki Koga
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Correspondence to Kenji Iohara.

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Communicated by I. Runkel.

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Iohara, K., Koga, Y. Enright functors for Kac-Moody superalgebras. Abh. Math. Semin. Univ. Hambg. 82, 205–226 (2012). https://doi.org/10.1007/s12188-012-0071-x

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  • DOI: https://doi.org/10.1007/s12188-012-0071-x

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