Integrability of invariant geodesic flows on \(n\)-symmetric spaces (Q708852)

The author considers the Ledger-Obata symmetric space \(Q=K^n/\mathrm{diag}(K)\), where \(K\) is a compact connected semisimple Lie group. It is shown that the geodesic flow of a normal metric (invariant Einstein metric) on the homogeneous space \(Q\) is Liouville integrable. The proof is based on modifying the argument shift method that allows to construct a complete set of polynomials, on the Lie algebra of \(K^n\), with respect to the usual Lie-Poisson bracket.