ON TYPE-I QUANTUM AFFINE SUPERALGEBRAS

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 in order to properly define U-q[sl(m\n)((1))] 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-parameter-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-parameter-like parameters, providing generalizations of the free fermion model.