Isotropic embeddings of coadjoint orbits and magnetic geodesic flows
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909608356872192 |
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| author | Bykov, Dmitri Kuzovchikov, Andrew |
| author_facet | Bykov, Dmitri Kuzovchikov, Andrew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isotropic embeddings of coadjoint orbits and magnetic geodesic flows Bykov, Dmitri Kuzovchikov, Andrew Differential Geometry High Energy Physics - Theory Mathematical Physics Symplectic Geometry 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. |
| title | Isotropic embeddings of coadjoint orbits and magnetic geodesic flows |
| topic | Differential Geometry High Energy Physics - Theory Mathematical Physics Symplectic Geometry |
| url | https://arxiv.org/abs/2503.08646 |