Algebraic nested Bethe ansatz for the elliptic Ruijsenaars model

1998/06/12 by E. Billey, Billey, E.
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/9806068

Latex2e file (with amsart.sty)

arxiv created 1998/06/12 · arxiv updated 2009/11/30

Abstract

The eigenvalues of the elliptic N-body Ruijsenaars operator are obtained by a dynamical version of the algebraic nested Bethe ansatz method. We use a result of Felder and Varchenko, who showed how to obtain the Ruijsenaars operator as the transfer matrix of a particular representation of the elliptic quantum group associated to gl(N).

Related

• Eigenvalues of Ruijsenaars–Schneider models associated with An−1 root system in Bethe ansatz formalism
• Elliptic solutions to difference non-linear equations and nested Bethe ansatz equations
• On separation of variables and completeness of the Bethe ansatz for quantum gl_N Gaudin model
• Solutions of the elliptic qKZB equations and Bethe ansatz I
• Incarnations of XXX \widehat\fraksl_N Bethe ansatz equations and integrable hierarchies