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Solutions of the Quantum-Yang-Baxter-Equation from Symmetric Spaces

M. Bordemann·M. Walter
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Abstract

We show that for each semi-Riemannian locally symmetric space the curvature tensor gives rise to a rational solution $r$ of the classical Yang-Baxter equation with spectral parameter. For several Riemannian globally symmetric spaces $M$ such as real, complex and quaternionic Grassmann manifolds we explicitly compute solutions $R$ of the quantum Yang Baxter equations (represented in the tangent spaces of $M$) which generalize the quantum $R$-matrix found by Zamolodchikov and Zamolodchikov in 1979.

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M. Bordemann, M. Walter. 2001-07-03. Solutions of the Quantum-Yang-Baxter-Equation from Symmetric Spaces. https://arxiv.org/abs/math/0107018

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