Slodowy slices and the complete integrability of Mishchenko-Fomenko subalgebras on regular adjoint orbits

2018/03/13 by Peter Crooks, Crooks, Peter, Stefan Rosemann +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.AG #math.DG #math.SG

paper · pdf · doi:10.48550/arxiv.1803.04942

arxiv created 2018/03/13 · arxiv updated 2018/03/14

Abstract

This work is concerned with Mishchenko-Fomenko subalgebras and their restrictions to the adjoint orbits in a finite-dimensional complex semisimple Lie algebra. In this setting, it is known that each Mishchenko-Fomenko subalgebra restricts to a completely integrable system on every orbit in general position. We improve upon this result, showing that each Mishchenko-Fomenko subalgebra yields a completely integrable system on all regular orbits (i.e. orbits of maximal dimension). Our approach incorporates the theory of regular \mathfraksl₂-triples and associated Slodowy slices, as developed by Kostant.

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