ON TYPE-I QUANTUM AFFINE SUPERALGEBRAS

The type I simple Lie superalgebras are sl(m\n) and osp(2\2n). We stud y 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 in order to properly define U-q[sl(m\n)((1))] and U-q[o sp(2\2n)((1))]. We present a general technique for deriving the spectr al-parameter-dependent R matrices from quantum affine superalgebras. W e determine the R matrices for the type I affine superalgebra U-q[sl(m \n)((1))] in various representations, thereby deriving new solutions o f the spectral-parameter-dependent Yang-Baxter equation. In particular , because this algebra possesses one-parameter families of finite-dime nsional irreps, we are able to construct R matrices depending on two a dditional spectral-parameter-like parameters, providing generalization s of the free fermion model.