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Pfaffian and Determinant Solutions to A Discretized Toda Equation for $B_r, C_r$ and $D_r$

Atsuo Kuniba·Shuichi Nakamura·Ryogo Hirota
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Abstract

We consider a class of 2 dimensional Toda equations on discrete space-time. It has arisen as functional relations in commuting family of transfer matrices in solvable lattice models associated with any classical simple Lie algebra $X_r$. For $X_r = B_r, C_r$ and $D_r$, we present the solution in terms of Pfaffians and determinants. They may be viewed as Yangian analogues of the classical Jacobi-Trudi formula on Schur functions.

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Atsuo Kuniba, Shuichi Nakamura, Ryogo Hirota. 1995-09-08. Pfaffian and Determinant Solutions to A Discretized Toda Equation for $B_r, C_r$ and $D_r$. https://doi.org/10.1088/0305-4470%2F29%2F8%2F022

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