BETHE ANSATZ AND QUANTUM GROUPS - THE LIGHT-CONE LATTICE APPROACH .1. 6 VERTEX AND SOS MODELS

The six-vertex model is solved with fixed boundary conditions (FBC) that guarantee exact SU(2), invariance on the lattice. The algebra of the Yang-Baxter (YB) and SU(2), generators turns to close and the transfer matrix is SU(2)q-invariant for FBC. In addition, the infinite spectral parameter limit of the YB generators yields cleanly the SU(2)q generators. The Bethe ansatz states constructed for FBC are shown to be the highest weights of SU(2)q. The light-cone evolution operator for FBC is introduced and shown to follow from the row-to-row FBC transfer matrix with alternating inhomogeneities. This operator is shown to describe the SOS model after an appropriate gauge choice. Using this FBC light-cone approach, the scaling limit of both six-vertex and SOS models easily follows. Finally, the higher level Bethe ansatz equations (describing the physical excitations) are explicitly derived for FBC.