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Quasifinite highest weight modules over the superW 1+∞algebra

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Abstract

We study quasifinite highest weight modules over the supersymmetric extension of theW 1+∞ algebra on the basis of the analysis by Kac and Radul. We find that the quasifiniteness of the modules is again characterized by polynomials, and obtain the differential equations for highest weights. The spectral flow, free field realization over the (B, C)-system, and the embedding into\(\widehat{gl}\)(∞|∞) are also presented.

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Authors and Affiliations

  1. Yukawa Institute for Theoretical Physics, Kyoto University, 606, Kyoto, Japan

    Hidetoshi Awata

  2. Yukawa Institute for Theoretical Physics, Kyoto University, 606, Kyoto, Japan

    Masafumi Fukuma

  3. Department of Physics, University of Tokyo, Bunkyo-ku, Hongo 7-3-1, 113, Tokyo, Japan

    Yutaka Matsuo

  4. Department of Physics, Faculty of Liberal Arts, Shinsku University, 390, Matsumoto, Japan

    Satoru Odake

Authors
  1. Hidetoshi Awata
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  2. Masafumi Fukuma
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  3. Yutaka Matsuo
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  4. Satoru Odake
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Additional information

Communicated by M. Jimbo

Address after April 1, 1994: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606, Japan

Address after April 1, 1994: Uji Research Center, Yukawa Institute for Theoretical Physics, Kyoto University, Uji 611, Japan

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Awata, H., Fukuma, M., Matsuo, Y. et al. Quasifinite highest weight modules over the superW 1+∞algebra. Commun.Math. Phys. 170, 151–179 (1995). https://doi.org/10.1007/BF02099443

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  • DOI: https://doi.org/10.1007/BF02099443

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