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arXiv · hep-th/9408006

On Type-I Quantum Affine Superalgebras

Gustav W. Delius·Mark D. Gould·Jon R. Links·Yao-Zhong Zhang
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Abstract

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.

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Gustav W. Delius, Mark D. Gould, Jon R. Links, Yao-Zhong Zhang. 1994-10-27. On Type-I Quantum Affine Superalgebras. https://doi.org/10.1142/s0217751x95001571

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