Yang-Baxter R operators and parameter permutations

Derkachov, S.; Karakhanyan, D.; Kirschner, R.

Yang-Baxter R operators and parameter permutations

Authors

Derkachov, S.

Karakhanyan, D.

Kirschner, R.

Description

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.
22 pages LaTex, comments added, version to be published in Nucl. Phys. B