Abstract
We discuss integrable models of quantum field theory and statistical mechanics. The dynamics and kinematics of these models are defined by Hamiltonians with symmetries determined by Lie algebras. The paper is devoted to the characterization of models such that the root vectors of their symmetry algebras run two orbits under the action of the Weyl group. Such properties possess root systems of the type B N , C N , and G 2. The main focus is on models with the symmetry of algebras B N . In this case the main characteristics of the process are obtained from the system of Yang-Baxter equation and the reflection equations.
We consider the Calogero-Moser and Calogero-Sutherland models and also the formalisms of the Lax and Dunkl operators. The connection between these formalisms and method of describing these models in terms of the generalized Knizhnik-Zamolodchikov equations with the system of roots of the type B N by the example of the Gaudin model with reflection are discussed. Examples of many-particle systems that interact with each other with reflections are presented.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 10, Suzdal Conference-4, 2003.
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Golubeva, V.A. Many-Particle Models with Two Constants of Interaction. J Math Sci 129, 3557–3565 (2005). https://doi.org/10.1007/s10958-005-0293-x
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DOI: https://doi.org/10.1007/s10958-005-0293-x