Integrable Systems and Poisson-Lie T-duality: a finite dimensional example

TL;DR

This paper explores the relationship between integrable models and Poisson-Lie T-duality using a finite-dimensional example based on SL(2,C), demonstrating how factorization and collective dynamics solve related systems.

Contribution

It provides a concrete finite-dimensional example illustrating the connection between integrable systems and Poisson-Lie T-duality, combining Adler-Kostant-Symes theory with factorization methods.

Findings

Demonstrates the solution of integrable systems via factorization in SL(2,C)

Shows the Toda system's relation to dynamics on SU(2) and B

Connects collective dynamics with Poisson-Lie T-duality

Abstract

We study the deep connection between integrable models and Poisson-Lie T-duality working on a finite dimensional example constructed on SL(2,C) and its Iwasawa factors SU(2) and B. We shown the way in which Adler-Kostant-Symes theory and collective dynamics combine to solve the equivalent systems from solving the factorization problem of an exponential curve in SL(2,C). It is shown that the Toda system embraces the dynamics of the systems on SU(2) and B.