On adjoint orbits in nilpotent ideals of a Borel subalgebra
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915470349697024 |
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| author | Yu, Rupert W. T. |
| author_facet | Yu, Rupert W. T. |
| contents | Let $\mathfrak{m}$ be a nilpotent ideal in the Borel subalgebra $\mathfrak{b}$ of a complex finite-dimensional semisimple Lie algebra, and $\mathfrak{m}^{\bullet}$ the subset of (ad-)nilpotent elements in $\mathfrak{b}$ such that $\mathfrak{m}$ is the minimal ideal containing them. This set is stable under the adjoint action of the corresponding Borel subgroup $B$. We prove that $\mathfrak{m}^{\bullet}$ contains a unique closed $B$-orbit which is the orbit of a nilpotent element whose support is the set of minimal roots associated to the root space decomposition of $\mathfrak{m}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21647 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On adjoint orbits in nilpotent ideals of a Borel subalgebra Yu, Rupert W. T. Representation Theory 17B20, 14L30 Let $\mathfrak{m}$ be a nilpotent ideal in the Borel subalgebra $\mathfrak{b}$ of a complex finite-dimensional semisimple Lie algebra, and $\mathfrak{m}^{\bullet}$ the subset of (ad-)nilpotent elements in $\mathfrak{b}$ such that $\mathfrak{m}$ is the minimal ideal containing them. This set is stable under the adjoint action of the corresponding Borel subgroup $B$. We prove that $\mathfrak{m}^{\bullet}$ contains a unique closed $B$-orbit which is the orbit of a nilpotent element whose support is the set of minimal roots associated to the root space decomposition of $\mathfrak{m}$. |
| title | On adjoint orbits in nilpotent ideals of a Borel subalgebra |
| topic | Representation Theory 17B20, 14L30 |
| url | https://arxiv.org/abs/2508.21647 |