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On the Sutherland spin model of B-N type and its associated spin chain

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Finkel Morgenstern, Federico and Gómez-Ullate Otaiza, David and González López, Artemio and Rodríguez González, Miguel Ángel and Zhdanov, R. (2003) On the Sutherland spin model of B-N type and its associated spin chain. Communications in mathematical physics, 233 (2). pp. 191-209. ISSN 0010-3616

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Official URL: http://dx.doi.org/10.1007/s00220-002-0742-z




Abstract

The B-N hyperbolic Sutherland spin model is expressed in terms of a suitable set of commuting Dunkl operators. This fact is exploited to derive a complete family of commuting integrals of motion of the model, thus establishing its integrability. The Dunkl operators are shown to possess a common flag of invariant finite-dimensional linear spaces of smooth scalar functions. This implies that the Hamiltonian of the model preserves a corresponding flag of smooth spin functions. The discrete spectrum of the restriction of the Hamiltonian to this spin flag is explicitly computed by triangularization. The integrability of the hyperbolic Sutherland spin chain of BN type associated with the dynamical model is proved using Polychronakos's "freezing trick".


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©Springer.
This work was partially supported by the DGES under grant PB98-0821. R. Zhdanov would like to acknowledge the financial support of the Spanish Ministry of Education and Culture during his stay at the Universidad Complutense de Madrid. The authors would also like to thank the referee for several helpful remarks.

Uncontrolled Keywords:Inverse-square exchange; Integrable systems; Dunkl operators; Knizhnik-zamolodchikov; Particle-systems; Calogero models; Body problems; Lie-algebras; Polynomials
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:30943
Deposited On:17 Jun 2015 14:06
Last Modified:10 Dec 2018 15:09

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