Generalized q-Onsager algebras and dynamical K-matrices

A procedure to construct K-matrices from the generalized q-Onsager algebra is proposed. This procedure extends the intertwiner techniques used to obtain scalar (c-number) solutions of the reflection equation to dynamical (non-c-number) solutions. It shows the relation between soliton non-preserving...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-01, Vol.45 (2), p.25201-17
Main Authors: Belliard, S, Fomin, V
Format: Article
Language:English
Subjects:
Algebra
Amplitudes
Boundaries
Degrees of freedom
dynamical boundary conditions
Exact sciences and technology
generalized
intertwiner equation
Mathematical analysis
Mathematical models
Mathematical Physics
Mathematics
Onsager algebra
Physics
Reflection
reflection algebras
Scalars
Texts
Zhedanov algebra
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Summary:A procedure to construct K-matrices from the generalized q-Onsager algebra is proposed. This procedure extends the intertwiner techniques used to obtain scalar (c-number) solutions of the reflection equation to dynamical (non-c-number) solutions. It shows the relation between soliton non-preserving reflection equations or twisted reflection equations and the generalized q-Onsager algebras. These dynamical K-matrices are important to quantum integrable models with extra degrees of freedom located at the boundaries; for instance, in the quantum affine Toda field theories on the half-line, they yield the boundary amplitudes. As examples, the cases of and are treated in detail.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/2/025201