Poisson-commutative subalgebras and complete integrability on non-regular coadjoint orbits and flag varieties

2019/02/25 by Panyushev, Dmitri I., Yakimova, Oksana S.
#14L30 #17B08 #17B20 #17B63 #22E46 #FOS: Mathematics #Representation Theory (math.RT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1902.09221

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.

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