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A new realization of the basic representation of A n (1)

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Abstract

The basic representation of A n (1) is constructed on a space of paths in ℤ(n + 1)ℤ. A q-analogue of this is also presented. Our construction gives a Lie theoretical proof of a combinatorial identity used in the evaluation of the local state probabilities for a class of solvable lattice models.

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Authors and Affiliations

  1. Department of Mathematics, College of General Education, Kyoto University, 606, Kyoto, Japan

    E. Date

  2. Research Institute for Mathematical Sciences, Kyoto University, 606, Kyoto, Japan

    M. Jimbo, T. Miwa & M. Okado

  3. Institute of Physics, College of Arts and Sciences, University of Tokyo, 153, Tokyo, Japan

    A. Kuniba

Authors
  1. E. Date
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  2. M. Jimbo
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  3. A. Kuniba
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  4. T. Miwa
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  5. M. Okado
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Date, E., Jimbo, M., Kuniba, A. et al. A new realization of the basic representation of A n (1) . Lett Math Phys 17, 51–54 (1989). https://doi.org/10.1007/BF00420014

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  • DOI: https://doi.org/10.1007/BF00420014

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