We present an uniform construction of the solution to the Yang- Baxter equation with the symmetry algebra sl(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 $l_1$ and $l_2$ is built in terms of products of three basic operators $S_1$, $S_2$, $S_3$ which are constructed explicitly. They have the simple meaning of representing elementary permutations of the symmetric group -- the permutation group of the four parameters entering the RLL-relation. As an illustration we consider the application to the construction of Baxter Q-operator.