Caudrelier, V orcid.org/0000-0003-0129-6758 and Crampé, N (2008) Symmetries of Spin Calogero Models. Symmetry, Integrability and Geometry : Methods and Applications, 4. 090. ISSN 1815-0659
Abstract
We investigate the symmetry algebras of integrable spin Calogero systems constructed from Dunkl operators associated to finite Coxeter groups. Based on two explicit examples, we show that the common view of associating one symmetry algebra to a given Coxeter group W is wrong. More precisely, the symmetry algebra heavily depends on the representation of W on the spins. We prove this by identifying two different symmetry algebras for a BL spin Calogero model and three for G2 spin Calogero model. They are all related to the half-loop algebra and its twisted versions. Some of the result are extended to any finite Coxeter group.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an open access article under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) |
Keywords: | Calogero models; symmetry algebra; twisted half-loop algebra |
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: | 23 Aug 2019 15:28 |
Last Modified: | 28 Aug 2019 08:17 |
Status: | Published |
Publisher: | National Academy of Science of Ukraine |
Identification Number: | 10.3842/SIGMA.2008.090 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:98348 |