(Quantum) twisted Yangians: symmetry, Baxterisation and centralizers

Abstract

Based on the (quantum) twisted Yangians, integrable systems with special boundary conditions, called soliton non-preserving (SNP), may be constructed. In the present article we focus on the study of subalgebras of the (quantum) twisted Yangians, and we show that such a subalgebra provides an exact symmetry of the rational transfer matrix. We discuss how the spectrum of a generic transfer matrix may be obtained by focusing only on two types of special boundaries. It is also shown that the subalgebras, emerging from the asymptotics of tensor product representations of the (quantum) twisted Yangian, turn out to be dual to the (quantum) Brauer algebra. To deal with general boundaries in the trigonometric case we propose a new algebra, which also provides the appropriate framework for the Baxterisation procedure in the SNP case.

23 pages, Latex. Minor typos correted, acknowledgments added. J. Math. Phys. Vol. 48 (2007), to appear

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Cited by in corpus (8)

• Set theoretic Yang-Baxter & reflection equations and quantum group symmetries
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• Integrable boundary conditions and modified Lax equations
• Boundary Lax pairs for the $A_n^{(1)}$ Toda field theories
• $A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited
• On boundary super algebras
• Contracted and expanded integrable structures
• Generalized Landau-Lifshitz models on the interval