Yang-Baxter R operators and parameter permutations

S. Derkachov; D. Karakhanyan; R. Kirschner

doi:10.1016/j.nuclphysb.2007.05.022

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arXiv · hep-th/0703076

Yang-Baxter R operators and parameter permutations

S. Derkachov·D. Karakhanyan·R. Kirschner

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Abstract

We present an uniform construction of the solution to the Yang- Baxter equation with the symmetry algebra $s\ell(2)$ and its deformations: the q-deformation and the elliptic deformation or Sklyanin algebra. The R-operator acting in the tensor product of two representations of the symmetry algebra with arbitrary spins $\ell_1$ and $\ell_2$ is built in terms of products of three basic operators $\mathcal{S}_1, \mathcal{S}_2,\mathcal{S}_3$ which are constructed explicitly. They have the simple meaning of representing elementary permutations of the symmetric group $\mathfrak{S}_4$, the permutation group of the four parameters entering the RLL-relation.

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S. Derkachov, D. Karakhanyan, R. Kirschner. 2007-06-01. Yang-Baxter R operators and parameter permutations. https://doi.org/10.1016/j.nuclphysb.2007.05.022

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