Algebraic nested Bethe ansatz for the elliptic Ruijsenaars model

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).

Latex2e file (with amsart.sty)

References in corpus (2)

• Quasiclassical asymptotics of solutions to the KZ equations
• On the affine analogue of Jack's and Macdonald's polynomials

Cited by in corpus (7)

• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_n)$ and its applications
• Eigenvalues of Ruijsenaars-Schneider models associated with $A_{n-1}$ root system in Bethe ansatz formalism
• Elliptic Ruijsenaars difference operators on bounded partitions
• On the eigenstates of the elliptic Calogero-Moser model
• The deformed Inozemtsev spin chain
• Creation operators and algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{o}_3)$
• Construction of the Bethe State for the $E_{\tau ,\eta }(s{o}_3)$ Elliptic Quantum Group