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Tropical R and Tau Functions

Atsuo Kuniba·Masato Okado·Taichiro Takagi·Yasuhiko Yamada
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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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Atsuo Kuniba, Masato Okado, Taichiro Takagi, Yasuhiko Yamada. 2003-03-27. Tropical R and Tau Functions. https://doi.org/10.1007/s00220-003-1015-1

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