  The type-I simple Lie-superalgebras are $sl(m|n)$ and $osp(2|2n)$. We study
the quantum deformations of their untwisted affine extensions
$U_q(sl(m|n)^{(1)})$ and $U_q(osp(2|2n)^{(1)})$. We identify additional
relations between the simple generators (``extra $q$-Serre relations") which
need to be imposed to properly define $\uqgh$ and $U_q(osp(2|2n)^{(1)})$. We
present a general technique for deriving the spectral parameter dependent
R-matrices from quantum affine superalgebras. We determine the R-matrices for
the type-I affine superalgebra $U_q(sl(m|n)^{(1)})$ in various representations,
thereby deriving new solutions of the spectral-dependent Yang-Baxter equation.
In particular, because this algebra possesses one-parameter families of
finite-dimensional irreps, we are able to construct R-matrices depending on two
additional spectral-like parameters, providing generalizations of the
free-fermion model.

High Energy Physics - Theory;Quantum Algebra