2000 character limit reached
Poisson-commutative subalgebras and complete integrability on non-regular coadjoint orbits and flag varieties (1902.09221v1)
Published 25 Feb 2019 in math.SG and math.RT
Abstract: The purpose of this paper is to bring together various loose ends in the theory of integrable systems. For a semisimple Lie algebra $\mathfrak g$, we obtain several results on completeness of homogeneous Poisson-commutative subalgebras of ${\mathcal S}(\mathfrak g)$ on coadjoint orbits. This concerns, in particular, Mishchenko-Fomenko and Gelfand-Tsetlin subalgebras.