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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 ..."
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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.
Two Equivalent Realizations of Trigonometric Dynamical Affine Quantum Group Uq,x(ŝl2) = Uq,λ(ŝl2), Drinfeld Currents and Hopf Algebroid Structures
, 2014
"... Two new realizations, denoted Uq,x(ĝl2) and U(Rq,x(ĝl2)) of the dynamical quantum affine algebra Uq,λ(ĝl2) are proposed, based on Drinfeldcurrents and RLL relations respectively, along with a Heisenberg algebra {P,Q}, with x = q2P. Here P plays the role of the dynamical variable λ and Q = ∂∂P. A ..."
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Two new realizations, denoted Uq,x(ĝl2) and U(Rq,x(ĝl2)) of the dynamical quantum affine algebra Uq,λ(ĝl2) are proposed, based on Drinfeldcurrents and RLL relations respectively, along with a Heisenberg algebra {P,Q}, with x = q2P. Here P plays the role of the dynamical variable λ and Q = ∂∂P. An explicit isomorphism from Uq,x(ĝl2) to U(Rq,x(ĝl2)) is established, which is a dynamical extension of the DingFrenkel isomorphism of Uq(ĝl2) with U(Rq(ĝl2)) between the Drinfeld realization and the ReshetikhinTianShanksy construction of quantum affine algebras. Hopf algebroid structures and an affine dynamical determinant element are introduced and it is shown that Uq,x(ŝl2) is isomorphic to U(Rq,x(ŝl2)). The dynamical construction is based on the degeneration of the elliptic quantum algebra Uq,p(ŝl2) of Jimbo, Konno et al. as the elliptic variable p → 0.