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arXiv · 0707.3036

On the semi-dynamical reflection equation: solutions and structure matrices

J. Avan·C. Zambon
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Abstract

Explicit solutions of the non-constant semi-dynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semi-dynamical reflection equation with rational non-constant Arutyunov-Chekhov-Frolov structure matrices, and a specific meromorphic ansatz, it is found that only two sets of the previously found constant solutions are extendible to the non-constant case. In order to simplify future constructions of spin-chain Hamiltonians, a parametrization procedure is applied explicitly to all elements of the semi-dynamical reflection equation available. Interesting expressions for `twists' and R-matrices entering the parametrization procedure are found. In particular, some expressions for the R-matrices seem to appear here for the first time. In addition, a new set of consistent structure matrices for the semi-dynamical reflection equation is obtained.

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J. Avan, C. Zambon. 2007-07-20. On the semi-dynamical reflection equation: solutions and structure matrices. https://doi.org/10.1088/1751-8113/41/19/194001

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