Superintegrability of Generalized Toda Models on Symmetric Spaces

TL;DR

This paper proves the superintegrability of Hamiltonian systems on symmetric spaces derived from simple Lie groups with Poisson structures, expanding understanding of integrable models in mathematical physics.

Contribution

It establishes superintegrability for a broad class of Hamiltonian systems on symmetric spaces associated with simple Lie groups, using Poisson geometry.

Findings

Superintegrability is proven for systems on $K\backslash G/K$.

The results apply to Hamiltonian systems restricted to symplectic leaves.

The work extends integrability theory in the context of Lie groups and symmetric spaces.

Abstract

In this paper we prove superintegrability of Hamiltonian systems generated by functions on $K\backslash G/K$, restriced to a symplectic leaf of the Poisson variety $G/K$, where $G$ is a simple Lie group with the standard Poisson Lie structure, $K$ is the subgroup of fixed points with respect to the Cartan involution.