Representation Theory and the Quantum Inverse Scattering Method: The Open Toda Chain and the Hyperbolic Sutherland Model

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dc.creatorGerasimov, A.
dc.creatorKharchev, S.
dc.creatorLebedev, D.
dc.date2002-04-16
dc.date2003-02-26
dc.date.accessioned2026-07-07T04:47:44Z
dc.date.available2026-07-07T04:47:44Z
dc.descriptionUsing the representation theory of $\frak{gl}(N,\RR)$, we express the wave function of the $GL(N,\RR)$ Toda chain, which two of us recently obtained by the Quantum Inverse Scattering Method, in terms of multiple integrals. The main tool is our generalization of the Gelfand-Zetlin method to the case of infinite-dimensional representations of $\frak{gl}(N,\RR)$. The interpretation of this generalized construction in terms of the coadjoint orbits is given and the connection with the Yangian $Y(\frak{gl}(N))$ is discussed. We also give the hyperbolic Sutherland model eigenfunctions expressed in terms of integrals in the Gelfand-Zetlin representation. Using the example of the open Toda chain, we discuss the connection between the Quantum Inverse Scattering Method and Representation Theory.
dc.descriptionAmsLaTex, 29 pages; small corrections are given; two examples and few references added
dc.identifierhttps://arxiv.org/abs/math/0204206
dc.identifierhttp://arxiv.org/abs/math/0204206
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63834
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectRepresentation Theory
dc.subjectExactly Solvable and Integrable Systems
dc.titleRepresentation Theory and the Quantum Inverse Scattering Method: The Open Toda Chain and the Hyperbolic Sutherland Model
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