Lie Groups, Cluster Variables and Integrable Systems
Abstract
We discuss the Poisson structures on Lie groups and propose an explicit construction of the integrable models on their appropriate Poisson submanifolds. The integrals of motion for the SL(N)-series are computed in cluster variables via the Lax map. This construction, when generalised to the co-extended loop groups, gives rise not only to several alternative descriptions of relativistic Toda systems, but allows to formulate in general terms some new class of integrable models.
Cite
@article{arxiv.1207.1869,
title = {Lie Groups, Cluster Variables and Integrable Systems},
author = {A. Marshakov},
journal= {arXiv preprint arXiv:1207.1869},
year = {2015}
}
Comments
Based on talks given at Versatility of integrability, Columbia University, May 2011; Simons Summer Workshop on Geometry and Physics, Stony Brook, July-August 2011; Classical and Quantum Integrable Systems, Dubna, January 2012; Progress in Quantum Field Theory and String Theory, Osaka, April 2012; Workshop on Combinatorics of Moduli Spaces and Cluster Algebras, Moscow, May-June 2012