Yang–Baxter image-operators and parameter permutations Original Research Article

We present an uniform construction of the solution to the Yang–Baxter equation with the symmetry algebra image and its deformations: the q-deformation and the elliptic deformation or Sklyanin algebra. The image-operator acting in the tensor product of two representations of the symmetry algebra with arbitrary spins image and image is built in terms of products of three basic operators image, image, image which are constructed explicitly. They have the simple meaning of representing elementary permutations of the symmetric group image, the permutation group of the four parameters entering the RLL-relation.