Yang-Baxter R operators and parameter permutations

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.

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

References in corpus (2)

• Summation, transformation, and expansion formulas for multibasic theta hypergeometric series
• Multiplication Formulas for the Elliptic Gamma Function

Cited by in corpus (1)

• Iterative construction of $U_q(s\ell (n+1))$ representations and Lax matrix factorisation