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arXiv · 1706.05819

Abstract integrable systems on hyperk\"ahler manifolds arising from Slodowy slices

Peter Crooks·Steven Rayan
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Abstract

We study holomorphic integrable systems on the hyperk\"ahler manifold $G\times S_{\text{reg}}$, where $G$ is a complex semisimple Lie group and $S_{\text{reg}}$ is the Slodowy slice determined by a regular $\mathfrak{sl}_2(\mathbb{C})$-triple. Our main result is that this manifold carries a canonical \textit{abstract integrable system}, a foliation-theoretic notion recently introduced by Fernandes, Laurent-Gengoux, and Vanhaecke. We also construct traditional integrable systems on $G\times S_{\text{reg}}$, some of which are completely integrable and fundamentally based on Mishchenko and Fomenko's argument shift approach.

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BibTeXRIS

Peter Crooks, Steven Rayan. 2017-06-19. Abstract integrable systems on hyperk\"ahler manifolds arising from Slodowy slices. https://doi.org/10.4310/mrl.2019.v26.n1.a2

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