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arXiv · 1803.04942

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

Peter Crooks·Stefan Rosemann·Markus Roeser
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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 $\mathfrak{sl}_2$-triples and associated Slodowy slices, as developed by Kostant.

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Peter Crooks, Stefan Rosemann, Markus Roeser. 2018-03-13. Slodowy slices and the complete integrability of Mishchenko-Fomenko subalgebras on regular adjoint orbits. https://arxiv.org/abs/1803.04942

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