Results 1 
4 of
4
Universal VertexIRF Transformation for Quantum Affine Algebras
, 2008
"... We construct a universal VertexIRF transformation between Vertex type universal solution and Face type universal solution of the quantum dynamical YangBaxter equation. This universal VertexIRF transformation satisfies the generalized coBoundary equation) case. This solution has a simple Gauss dec ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
We construct a universal VertexIRF transformation between Vertex type universal solution and Face type universal solution of the quantum dynamical YangBaxter equation. This universal VertexIRF transformation satisfies the generalized coBoundary equation) case. This solution has a simple Gauss decomposition which is constructed using Sevostyanov’s characters of twisted quantum Borel algebras. We show that the evaluation of this universal solution in the evaluation representation of Uq(A (1) 1) gives the standard Baxter’s transformation between the 8Vertex model and the IRF height model. and is an extension of our previous work to the quantum affine Uq(A (1) r 1
On the semidynamical reflection equation: solutions and structure matrices
, 707
"... Explicit solutions of the nonconstant semidynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semidynamical reflection equation with rational nonconstant ArutyunovChekhovFrolov structure matrices, and a specific me ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Explicit solutions of the nonconstant semidynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semidynamical reflection equation with rational nonconstant ArutyunovChekhovFrolov structure matrices, and a specific meromorphic ansatz, it is found that only two sets of the previously found constant solutions are extendible to the nonconstant case. In order to simplify future constructions of spinchain Hamiltonians, a parametrization procedure is applied explicitly to all elements of the semidynamical reflection equation available. Interesting expressions for ‘twists ’ and Rmatrices entering the parametrization procedure are found. In particular, some expressions for the Rmatrices seem to appear here for the first time. In addition, a new set of consistent structure matrices for the semidynamical reflection equation is obtained.