SO(4) SYMMETRY OF THE TRANSFER-MATRIX FOR THE ONE-DIMENSIONAL HUBBARD-MODEL

The SO(4) invariance of the transfer matrix for the one-dimensional Hu bbard model is clarified from the viewpoint of the quantum inverse sca ttering method. We demonstrate the SO(4) symmetry by means of the ferm ionic L-operator and the fermionic R-matrix, which satisfy the graded Yang-Baxter relation. The transformation law of the fermionic L-operat or under the SO(4) rotation is identified with a kind of gauge transfo rmation, which determines the corresponding transformation of the ferm ionic creation and annihilation operators under the SO(4) rotation. Th e transfer matrix is confirmed to be invariant under the SO(4) rotatio n, which ensures the SO(4) invariance of the conserved currents includ ing the Hamiltonian. Furthermore, we show that the representation of t he higher conserved currents in terms of the Clifford algebra gives ma nifestly SO(4) invariant forms.