BETHE ANSATZ AND QUANTUM GROUPS - THE LIGHT-CONE APPROACH .2. FROM RSOS(P+1) MODELS TO P-RESTRICTED SINE-GORDON FIELD-THEORIES

We solve the RSOS(p) models on the light-cone lattice with fixed boundary conditions by disentangling the type-II representations of SU(2)q, at q = e(ipi/p), from the full SOS spectrum obtain through algebraic Bethe ansatz. The rule which realizes the quantum group reduction to the RSOS states is that there must no be singular roots in the solutions of the Bethe ansatz equations describing the states with quantum spin J < (p - 1)/2. By studying how this rule is active on the particle states, we are able to give a microscopic derivation of the lattice S-matrix of the massive kinks. The correspondence between the light-cone six-vertex model and the sine-Gordon field theory implies that the continuum limit of the RSOS(p + 1) model is to be identified with the p-restricted sine-Gordon field theory.