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arXiv · 2503.08646

Isotropic embeddings of coadjoint orbits and magnetic geodesic flows

Dmitri Bykov·Andrew Kuzovchikov
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Abstract

We consider isotropic and Lagrangian embeddings of coadjoint orbits of compact Lie groups into products of coadjoint orbits. After reviewing the known facts in the case of $\mathrm{SU}(n)$ we initiate a similar study for $\mathrm{SO}$ and $\mathrm{Sp}$ cases. In the second part we apply this to the study of dynamical systems with $\mathrm{SU}(n)$ symmetry, proving equivalence between systems of two types: those describing magnetic geodesic flow on flag manifolds and classical `spin chains' of a special type.

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Dmitri Bykov, Andrew Kuzovchikov. 2025-03-11. Isotropic embeddings of coadjoint orbits and magnetic geodesic flows. https://arxiv.org/abs/2503.08646

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