Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of compact Lie groups

Abstract

The reduction of the `master system' of free motion on the cotangent bundle $T^{\ast }G$ 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 $T^{\ast }G/G$, 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.

14 pages, v2: corrected equation (4.54), simplified the proof of Lemma A.1 and removed typos, v3: updated references and removed newly noticed typos (equations unchanged)

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