Fehér, L and Görbe, TF (2014) Duality between the trigonometric BCn Sutherland system and a completed rational Ruijsenaars–Schneider–van Diejen system. Journal of Mathematical Physics, 55 (10). 102704. ISSN 0022-2488
Abstract
We present a new case of duality between integrable many-body systems, where two systems live on the action-angle phase spaces of each other in such a way that the action variables of each system serve as the particle positions of the other one. Our investigation utilizes an idea that was exploited previously to provide group-theoretic interpretation for several dualities discovered originally by Ruijsenaars. In the group-theoretic framework, one applies Hamiltonian reduction to two Abelian Poisson algebras of invariants on a higher dimensional phase space and identifies their reductions as action and position variables of two integrable systems living on two different models of the single reduced phase space. Taking the cotangent bundle of U(2n) as the upstairs space, we demonstrate how this mechanism leads to a new dual pair involving the BCn trigonometric Sutherland system. Thereby, we generalize earlier results pertaining to the An trigonometric Sutherland system as well as a recent work by Pusztai on the hyperbolic BCn Sutherland system.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 AIP Publishing LLC. Reproduced in accordance with the publisher's self-archiving policy. |
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) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Feb 2019 11:43 |
Last Modified: | 25 Jun 2023 21:41 |
Status: | Published |
Publisher: | AIP Publishing |
Identification Number: | 10.1063/1.4898077 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:141547 |