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 Uq(sl(m|n) (1)) and Uq(osp(2|2n) (1)). We identify additional relations between the simple generators (“extra q-Serre relations”) which need to be imposed to properly defineUq(sl(m|n) (1)) and Uq(osp(2|2n) (1)). We present a general technique for deriving the spectral parameter dependent Rmatrices from quantum affine superalgebras. We determine the R-matrices for the type-I affine superalgebra Uq(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. Supported by Habilitationsstipendium der Deutschen Forschungsgesellschaft On leave from Department of Physics, Bielefeld University, Germany