Notes on the Degenerate Integrability of Reduced Systems Obtained from the Master Systems of Free Motion on Cotangent Bundles of Compact Lie Groups

The reduction of the “master system” of free motion on the cotangent bundle \(T^*G\) of a compact, connected, and simply connected, semisimple Lie group is considered using the conjugation action of G. It is proved that the restriction of the reduced system to the smooth component of the quotient space \(T^*G/G\) , given by the principal orbit type, inherits the degenerate integrability of the master system. The proof can be generalized easily to other interesting examples of Hamiltonian reduction.