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Character and determinant formulae of quasifinite representation of theW 1+∞ algebra

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Abstract

We diagonalize the Hilbert space of some subclass of the quasifinite module of theW 1+∞ algebra. States are classified according to their eigenvalues for infinitely many commuting charges and the Young diagrams. The parameter dependence of their norms is explicitly derived. The full character formulae of the degenerate representations are given as summation of the bilinear combinations of the Schur polynomials.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, 606-01, Kyoto, Japan

    H. Awata

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

    M. Fukuma

  3. Uji Research Center, Yukawa Institute for Theoretical Physics, Kyoto University, 611, Uji, Japan

    Y. Matsuo

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

    S. Odake

Authors
  1. H. Awata
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  2. M. Fukuma
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  3. Y. Matsuo
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  4. S. Odake
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Communicated by M. Jimbo

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Awata, H., Fukuma, M., Matsuo, Y. et al. Character and determinant formulae of quasifinite representation of theW 1+∞ algebra. Commun.Math. Phys. 172, 377–400 (1995). https://doi.org/10.1007/BF02099433

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  • DOI: https://doi.org/10.1007/BF02099433

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