Twisted Quantum Affine Superalgebra $U_q[sl(2|2{)}^{(2)}]$, $U_q[osp(2|2)]$ Invariant R-matrices and a New Integrable Electronic Model

Abstract

We describe the twisted affine superalgebra $sl(2|2{)}^{(2)}$ and its quantized version $U_q[sl(2|2{)}^{(2)}]$. We investigate the tensor product representation of the 4-dimensional grade star representation for the fixed point subsuperalgebra $U_q[osp(2|2)]$. We work out the tensor product decomposition explicitly and find the decomposition is not completely reducible. Associated with this 4-dimensional grade star representation we derive two $U_q[osp(2|2)]$ invariant R-matrices: one of them corresponds to $U_q[sl(2|2{)}^{(2)}]$ and the other to $U_q[osp(2|2{)}^{(1)}]$. Using the R-matrix for $U_q[sl(2|2{)}^{(2)}]$, we construct a new $U_q[osp(2|2)]$ invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly, this model reduces, in the $q=1$ limit, to the one proposed by Essler et al which has a larger, $sl(2|2)$, symmetry.

17 pages, LaTex file

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