Year: 2008
Type: article
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.
Authors: J Avan, C Zambon
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1995966528