Caudrelier, V orcid.org/0000-0003-0129-6758 and Crampé, N (2019) Classical N-reflection equation and Gaudin models. Letters in Mathematical Physics, 109 (4). pp. 843-856. ISSN 0377-9017
Abstract
We introduce the notion of N-reflection equation which provides a generalization of the usual classical reflection equation describing integrable boundary conditions. The latter is recovered as a special example of the N=2 case. The basic theory is established and illustrated with several examples of solutions of the N-reflection equation associated with the rational and trigonometric r-matrices. A central result is the construction of a Poisson algebra associated with a non-skew-symmetric r-matrix whose form is specified by a solution of the N-reflection equation. Generating functions of quantities in involution can be identified within this Poisson algebra. As an application, we construct new classical Gaudin-type Hamiltonians, particular cases of which are Gaudin Hamiltonians of BCL-type.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018, The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
Keywords: | Classical Yang–Baxter equation; Classical reflection equation; Gaudin models; Non-skew-symmetric r-matrices |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 16 Oct 2018 10:14 |
Last Modified: | 25 Jun 2023 21:32 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s11005-018-1128-2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:137085 |
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