Solutions to the Yang-Baxter equations with $osp_q(1|2)$ symmetry: Lax operators

Details Solutions to the Yang-Baxter equations with $osp_q(1|2)$ symmetry: Lax operators Solutions to the Yang-Baxter equations with $osp_q(1|2)$ symmetry: Lax operators

2008-06-17

arxiv.org/abs/0806.2781v2

Nuclear Physics B 808 [FS] (2009) 525-545

Physics

Mathematical Physics

22 pages; references added, minor corrections done

Scientific paper

10.1016/j.nuclphysb.2008.09.001

We find a new $4\times4$ solution to the $osp_q(1|2)$-invariant Yang-Baxter equation with simple dependence on the spectral parameter and propose $2\times 2$ matrix expressions for the corresponding Lax operator. The general inhomogeneous universal spectral-parameter dependent $R$-matrix is derived. It is proven, that there are two independent solutions to the homogeneous $osp_q(1|2)$-invariant YBE, defined on the fundamental three dimensional representations. One of them is the particular case of the universal matrix, while the second one does not admit generalization to the higher dimensional cases. Also the $3 \times 3$ matrix expression of the Lax operator is found, which have a well defined limit at $q \to 1$.

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