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Pfaffian and determinant solutions to a discretized Toda equation for \(B_r\), \(C_r\) and \(D_r\). (English) Zbl 0914.39001

Summary: We consider a class of two-dimensional Toda equations on discrete spacetime. It has arisen as functional relations in a 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.

MSC:

39A10 Additive difference equations
81T25 Quantum field theory on lattices
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