Abstract
We construct the family of spin-chain Hamiltonians, which have affine quantum group symmetry Uqĝ. Their eigenvalues coincide with the eigenvalues of the usual spin-chain Hamiltonians, but have the degeneracy of levels, corresponding to affine Uqĝ. The space of states of these spin-chains is formed by the tensor product of fully reducible representations. The fermionic representations of spin-chain Hamiltonians, which have affine quantum group symmerty, was consructed. They correspond to new extensions of Hubbard Hamiltonians. The exact ground state of some examples is presented, exhibiting superconducting behavior via η-pairing mechanism.
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