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This is a Quantitative Study study.

September 29, 2025Open Access

Isotropic embeddings of coadjoint orbits and magnetic geodesic flows

DBDmitri BykovRussian Academy of Sciences AKAndrew KuzovchikovRussian Academy of Sciences

Key Points

The study establishes a link between isotropic embeddings and magnetic geodesic flow in compact Lie groups.
It reveals that systems depicting magnetic geodesic flow on flag manifolds are equivalent to specific spin chains.
The investigation extends known results from SU(n) to include SO and Sp cases, broadening the scope of the analysis.
Application of the findings enhances our understanding of dynamical systems with SU(n) symmetry, implying new relationships.

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 SU (n) we initiate a similar study for SO and Sp cases. In the second part we apply this to the study of dynamical systems with 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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Cite This Study

Bykov et al. (Tue,) studied this question.

synapsesocial.com/papers/68da58d1c1728099cfd10b9d https://doi.org/https://doi.org/10.48550/arxiv.2503.08646