Action-angle map and duality for the open Toda lattice in the perspective of Hamiltonian reduction

Abstract: An alternative derivation of the known action-angle map of the standard open Toda lattice is presented based on its identification as the natural map between two gauge slices in the relevant symplectic reduction of the cotangent bundle of $GL(n,{{\mathbb R}})$. This then permits to interpret Ruijsenaars' action-angle duality for the Toda system in the same group-theoretic framework which was established previously for Calogero type systems.