Last update: 18 April 2014
This is an excerpt of the paper The Potts model and the symmetric group by V.F.R. Jones. It appeared in: Subfactors: Proceedings of the Taniguchi Symposium on Operator Algebras (Kyuzeso, 1993), River Edge, NJ, World Sci. Publishing, 1994, pp. 259–267.
The symmetric group acts on a vector space of dimension by permuting the basis elements The groups acts on by permuting the tensor product factors. We show that the algebra of all matrices on commuting with is generated by and the operators and where The matrices and give the vertical and horizontal transfer matrices adding one site in the square lattice 2-dimensional Potts model.