Poisson-commutative subalgebras and complete integrability on non-regular coadjoint orbits and flag varieties
Abstract
The purpose of this paper is to bring together various loose ends in the theory of integrable systems. For a semisimple Lie algebra g, we obtain several results on completeness of homogeneous Poisson-commutative subalgebras of S( g) on coadjoint orbits. This concerns, in particular, Mishchenko-Fomenko and Gelfand-Tsetlin subalgebras.
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