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Tropical R and Tau Functions

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Abstract

Tropical R is the birational map that intertwines products of geometric crystals and satisfies the Yang-Baxter equation. We show that the D (1) n tropical R introduced by the authors and its reduction to A (2) 2n−1 and C (1) n are equivalent to a system of bilinear difference equations of Hirota type. Associated tropical vertex models admit solutions in terms of tau functions of the BKP and DKP hierarchies.

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Authors and Affiliations

  1. Institute of Physics, University of Tokyo, Tokyo, 153-8902, Japan

    A. Kuniba

  2. Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, Osaka, 560-8531, Japan

    M. Okado

  3. Department of Applied Physics, National Defense Academy, Kanagawa, 239-8686, Japan

    T. Takagi

  4. Department of Mathematics, Faculty of Science, Kobe University, Hyogo, 657-8501, Japan

    Y. Yamada

Authors
  1. A. Kuniba
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  2. M. Okado
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  3. T. Takagi
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  4. Y. Yamada
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Correspondence to A. Kuniba.

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Communicated by L. Takhtajan

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Kuniba, A., Okado, M., Takagi, T. et al. Tropical R and Tau Functions. Commun. Math. Phys. 245, 491–517 (2004). https://doi.org/10.1007/s00220-003-1015-1

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