Family of Affine Quantum Group Invariant Integrable Extensions of Hubbard Hamiltonian

We construct the family of spin chain hamiltonians, which have affine quantum group symmetry U q ˆ g. Their eigenvalues coincide with the eigen-values of the usual spin chain hamiltonians, but have the degeneracy of levels, corresponding to affine U q ˆ g. The space of states of these spin chains is formed by the tensor product of fully reducible representations. The fermionic representations of constructed spin chain hamiltonians show that we have new extensions of Hubbard one-(or multi)-band hamil-tonians. All of them are integrable and have affine quantum group symmetry. The exact ground state of some examples is presented, exhibiting superconducting behavior via η-pairing mechanism.