J Avan and C Zambon 2008 J. Phys. A: Math. Theor. 41 194001 doi:10.1088/1751-8113/41/19/194001
J Avan and C Zambon
Show affiliationsExplicit 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.
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
Issue 19 (16 May 2008)
Received 31 July 2007
Published 29 April 2008
J Avan and C Zambon 2008 J. Phys. A: Math. Theor. 41 194001
A Poole et al 2007 J. Phys.: Condens. Matter 19 452201
2009 Meas. Sci. Technol. 20 129901
J Kiukas et al 2008 J. Phys. A: Math. Theor. 41 175206
Jari Rosti et al 2009 J. Phys. D: Appl. Phys. 42 214013
Xiang-Guo Meng et al 2008 J. Phys. A: Math. Theor. 41 235208
J R Torgerson and L Mandel 1998 Phys. Scr. 1998 110
Daniel Bonamy 2009 J. Phys. D: Appl. Phys. 42 214014
M Shimoda and H R Sharma 2008 J. Phys.: Condens. Matter 20 314008
Iwan Jensen J. Stat. Mech. (2009) P02065