(Quantum) twisted Yangians: Symmetry, Baxterisation, and centralizers

Journal Article · Thu Feb 15 04:00:00 EST 2007 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2437851· OSTI ID:20929647

Crampe, Nicolas; Doikou, Anastasia ^[1]

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1. International School for Advanced Studies, Via Beirut 2-4, 34014 Trieste (Italy) and Istituto Nazionale di Fisica Nucleare, Sezione di Trieste (Italy)

Based on the (quantum) twisted Yangians, integrable systems with special boundary conditions, called soliton nonpreserving (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.

• OSTI ID: 20929647
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 2 Vol. 48; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BOUNDARY CONDITIONS
INTEGRAL CALCULUS
MATRICES
QUANTUM MECHANICS
SOLITONS
SYMMETRY
TENSORS