Cyclic representations of the periodic Temperley Lieb algebra, complex   Virasoro representations and stochastic processes
  An $N$ ${L} \choose {L/2}$-dimensional representation of the periodic Temperley-Lieb algebra $TL_L(x)$ is presented. It is also a representation of the cyclic group $Z_N$. We choose $x = 1$ and define a Hamiltonian as a sum of the generators of the algebra acting in this representation. This Hamiltonian gives the time evolution operator of a stochastic process. In the finite-size scaling limit, the spectrum of the Hamiltonian contains representations of the Virasoro algebra with complex highest weights. The $N = 3$ case is discussed in detail. One discusses shortly the consequences of the existence of complex Virasoro representations on the physical properties of the systems. 
Francisco C. Alcaraz, Arum Ram and Vladimir Rittenberg
cond-mat.stat-mech math-ph math.MP