Integrable quantum systems and classical Lie algebras
We obtain six new infinite series of trigonometric solutions to triangle equations (quantum R-matrices) associated with the nonexceptional simple Lie algebras: \(s\ell (N)\), sp(N), o(N). The R-matrices are given in two equivalent representations: in an additive one (as a sum of poles with matrix coefficients) and in a multiplicative one (as a ratio of entire matrix functions). These R-matrices provide an exact integrability of anisotropic generalizations of \(s\ell (N)\), sp(N), o(N) invariant one- dimensional lattice magnetics and two-dimensional periodic Toda lattices associated with the above algebras.
trigonometric solutions to triangle equations
scientific article; zbMATH DE number 4024366
scientific article