2002/04/16 by A. Gerasimov, Gerasimov, A., S. Kharchev +4 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #hep-th #math.QA #math.RT #nlin.SI
paper · pdf · doi:10.48550/arxiv.math/0204206
AmsLaTex, 29 pages; small corrections are given; two examples and few references added
openalex publication_date 2002/04/16 · arxiv created 2003/02/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the representation theory of \frakgl(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 \frakgl(N,\RR). The interpretation of this generalized construction in terms of the coadjoint orbits is given and the connection with the Yangian Y(\frakgl(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.