Representation theory and quantum inverse scattering method: Open Toda chain and hyperbolic Sutherland model
Apr, 2002
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Abstract:
Using 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 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.References(30)
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