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Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials

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Abstract

We present an explicit formula of the Virasoro singular vectors in terms of Jack symmetric polynomials. The parametert in the Virasoro central chargec=13-6(t+1/t) is just identified with the deformation parameter α of Jack symmetric polynomialsJ γ(α). As a by-product, we obtain an integral representation of Jack symmetric polynomials indexed by the rectangular Young diagrams.

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Authors and Affiliations

  1. Department of Mathematics, Kyushu University, 812, Hakozaki, Fukuoka, Japan

    Katsuhisa Mimachi & Yasuhiko Yamada

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  1. Katsuhisa Mimachi
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  2. Yasuhiko Yamada
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Communicated by M. Jimbo

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Mimachi, K., Yamada, Y. Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials. Commun.Math. Phys. 174, 447–455 (1995). https://doi.org/10.1007/BF02099610

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  • DOI: https://doi.org/10.1007/BF02099610

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