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The semi-dynamical reflection equation: solutions and structure matrices

J Avan and C Zambon

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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.


PACS

03.65.Fd Algebraic methods

02.10.Ud Linear algebra

02.20.Sv Lie algebras of Lie groups

MSC

22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)

81Rxx Groups and algebras in quantum theory

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 19 (16 May 2008)

Received 31 July 2007

Published 29 April 2008



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