Results on the symmetries of integrable fermionic models on chains

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We investigate integrable fermionic models within the scheme of the graded Quantum Inverse Scattering Method, and prove that any symmetry imposed on the solution of the Yang-Baxter Equation reflects on the constants of motion of the model; generalizations with respect to known results are discussed. This theorem is shown to be very effective when combined with the Polynomial -matrix Technique (PRT): we apply both of them to the study of the extended Hubbard models, for which we find all the subcases enjoying several kinds of (super)symmetries. In particular, we derive a geometrical construction expressing any gl(2,1)-invariant model as a linear combination of EKS and U-supersymmetric models. Furtherly, we use the PRT to obtain 32 integrable so(4)-invariant models. By joint use of the Sutherland's Species technique and η-pairs construction we propose a general method to derive their physical features, and we provide some explicit results.