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The t-J model with constant t and J between any pair of sites is studied by exploiting the symmetry of the Hamiltonian with respect to site permutations. For a given number of electrons and a given total spin the exchange term simply yields an additive constant. Therefore the real problem is to diagonalize the "t- model", or equivalently the infinite U Hubbard Hamiltonian. Using extensively the properties of the permutation group, we are able to find explicitly both the energy eigenvalues and eigenstates, labeled according to spin quantum numbers and Young diagrams. As a corollary we also obtain the degenerate ground states of the finite $U$ Hubbard model with infinite range hopping -t>0.
Comment: 4 pages, Revtex, with 3 figures embedded in the text
Comment: RevTeX 4, 18 pages, 11 Encapsulated Postscript figures (v2) fig. 9 replaced for compatibility with PDF generation (v3) new references added
Comment: 9 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1008.2117
Comment: v2: 5 pages, 5 figures. Figure added and text edited to match published version. v1: 5 pages, 4 figures
Comment: Reprint to improve access. 13 pages, 6 figures.
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