Abstract
The author shows explicitly that the representation of a finite-dimensional algebra associated with the largest eigenvalues of the four-site transfer matrix for the q-state Potts model is reducible at the first irrational Beraha q value. He shows this fits into a pattern of reducibility at the Beraha values so that the asymptotic dimensionality of representations for large lattice width n is qn. For other q values the asymptotic dimensionality is 4n (q>4) or Kn with K>q(0<q<4).
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