Multiplicative integrable models from Poisson–Nijenhuis structures

Hidden geometrical structures in integrable models

The bootstrap equations for the ADE series of purely elastic scattering theories have turned out to be intimately connected with the geometry of root systems and the Coxeter element. An informal review of some of this material is given, mentioning also a couple of other contexts – the Pasquier models, and the simply-laced affine Toda field theories – where similar structures are encountered. Th...

New Integrable Models from Fusion

Integrable multistate or multiflavor/color models were recently introduced. They are generalizations of models corresponding to the defining representations of the Uq( ̂ sl(m)) quantum algebras. Here I show that a similar generalization is possible for all higher dimensional representations. The R-matrices and the Hamiltonians of these models are constructed by fusion. The sl(2) case is treated ...

Lie Algebraic Structures in Integrable Models, Affine Toda Field Theory

Integrable Models From Twisted Half Loop Algebras

This paper is devoted to the construction of new integrable quantum-mechanical models based on certain subalgebras of the half loop algebra of gl N . Various results about these subalgebras are proven by presenting them in the notation of the St Petersburg school. These results are then used to demonstrate the integrability, and find the symmetries, of two types of physical system: twisted Gaud...

Contracted and expanded integrable structures

We propose a generic framework to obtain certain types of contracted and centrally extended algebras. This is based on the existence of quadratic algebras (reflection algebras and twisted Yangians), naturally arising in the context of boundary integrable models. A quite old paradox concerning the“expansion” of the E2 algebra into sl2 is resolved using the representation theory of the aforementi...