Exact Solution of the general Non Intersecting String Model

We present a thorough analysis of the Non Intersecting String (NIS) model and its exact solution. This is an integrable $q$-states vertex model describing configurations of non-intersecting polygons on the lattice. The exact eigenvalues of the transfer matrix are found by analytic Bethe Ansatz. The Bethe Ansatz equations thus found are shown to be equivalent to those for a mixed spin model involving both 1/2 and infinite spin. This indicates that the NIS model provides a representation of the quantum group $SU(2)_{\hat q}$ ($|\hat q|\not= 1$) corresponding to spins $s=1/2$ and $s=\infty$. The partition function and the excitations in the thermodynamic limit are computed.