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

Kuniba, Atsuo; Nakamura, Shuichi; Hirota, Ryogo

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

Authors

Kuniba, Atsuo

Nakamura, Shuichi

Hirota, Ryogo

Description

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