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Integrable quantum systems and classical Lie algebras

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Abstract

We have obtained six new infinite series of trigonometric solutions to triangle equations (quantumR-matrices) associated with the nonexceptional simple Lie algebras:sl(N),sp(N),o(N). TheR-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). TheseR-matrices provide an exact integrability of anisotropic generalizations ofsl(N),sp(N),o(N) invariant one-dimensional lattice magnetics and two-dimensional periodic Toda lattices associated with the above algebras.

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  1. Institute for High Energy Physics, Serpukhov, Moscow Region, USSR

    V. V. Bazhanov

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Communicated by Ya. G. Sinai

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Bazhanov, V.V. Integrable quantum systems and classical Lie algebras. Commun.Math. Phys. 113, 471–503 (1987). https://doi.org/10.1007/BF01221256

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