Kuniba, Atsuo; Nakamura, Shuichi; Hirota, Ryogo Pfaffian and determinant solutions to a discretized Toda equation for \(B_r\), \(C_r\) and \(D_r\). (English) Zbl 0914.39001 J. Phys. A, Math. Gen. 29, No. 8, 1759-1766 (1996). 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. Cited in 8 Documents MSC: 39A10 Additive difference equations 81T25 Quantum field theory on lattices Keywords:two-dimensional Toda equations; Pfaffians; Yangian; difference equations; lattice models; Lie algebra; determinants; Jacobi-Trudi formula; Schur functions PDFBibTeX XMLCite \textit{A. Kuniba} et al., J. Phys. A, Math. Gen. 29, No. 8, 1759--1766 (1996; Zbl 0914.39001) Full Text: DOI arXiv