New solutions to the $s\ell_q(2)$-invariant Yang-Baxter equations at roots of unity

Details New solutions to the $s\ell_q(2)$-invariant Yang-Baxter equations at roots of unity New solutions to the $s\ell_q(2)$-invariant Yang-Baxter equations at roots of unity

2010-12-29

arxiv.org/abs/1012.5900v2

Nucl.Phys.B850:522-552,2011

Physics

Mathematical Physics

Improved and corrected; version to appaer in NUPHB

Scientific paper

10.1016/j.nuclphysb.2011.05.004

We find new solutions to the Yang-Baxter equations with the $R$-matrices possessing $sl_q(2)$ symmetry at roots of unity, using indecomposable representations. The corresponding quantum one-dimensional chain models, which can be treated as extensions of the XXZ model at roots of unity, are investigated. We consider the case $q^4=1$. The Hamiltonian operators of these models as a rule appear to be non-Hermitian. Taking into account the correspondence between the representations of the quantum algebra $sl_q(2)$ and the quantum super-algebra $osp_t(1|2)$, the presented analysis can be extended to the latter case for the appropriate values of the deformation parameter.

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