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

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.

Plain Tex, 9 pages

References in corpus (4)

• Quantum Jacobi-Trudi and Giambelli Formulae for $U_q(B_r^{(1)})$ from Analytic Bethe Ansatz
• Functional Relations in Solvable Lattice Models II
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• Discrete Toda Field Equations

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