On the Darboux-Nijenhuis variables for the open Toda lattice (Q2472026)

The authors compare two known families of the separated variables for the open Toda lattice with the corresponding Darboux-Nijenhuis coordinates. For the open Toda lattices associated with the root system \(A_n\) type the authors prove that the Moser variables are special Darboux-Nijenhuis variables, while the Sklyanin variables are ``almost Darboux-Nijenhuis variables'', in which recursion operator consists of a diagonal part and two non-diagonal rows and columns only.