New solutions to the $s{\ell }_q(2)$-invariant Yang-Baxter equations at roots of unity

Abstract

We find new solutions to the Yang-Baxter equations with the $R$-matrices possessing $s{l}_q(2)$ 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 $s{l}_q(2)$ and the quantum super-algebra $os{p}_t(1|2)$, the presented analysis can be extended to the latter case for the appropriate values of the deformation parameter.

Improved and corrected; version to appaer in NUPHB

References in corpus (3)

• Time evolution of non-Hermitian Hamiltonian systems
• Solutions to the Yang-Baxter equations with $os{p}_q(1|2)$ symmetry: Lax operators
• Fusion Rules of the Lowest Weight Representations of osp_q(1|2) at Roots of Unity: Polynomial Realization and Degeneration at Roots of Unity