Superintegrability of Generalized Toda Models on Symmetric Spaces

Abstract

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