A connection between minimal nilpotent orbits of types A and D via Hamiltonian reduction
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913146024755200 |
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| author | Fu, Baohua Liu, Jie |
| author_facet | Fu, Baohua Liu, Jie |
| contents | We establish a novel connection between the minimal nilpotent orbit $\mathbb{O}_n$ in $\mathfrak{sl}_n$ and the minimal nilpotent orbit closure $\overline{\mathbf{O}}_n$ in $\mathfrak{so}_{2n+2}$, which differs from the shared-orbit paradigm of Brylinski and Kostant, where no direct type-A--type-D relation appears. More precisely, we show that the affine closure of the cotangent bundle $\overline{T^*\mathbb{O}_n}^{\mathrm{aff}}$ is isomorphic to a $\mathbb{C}^*$-Hamiltonian reduction of $\overline{\mathbf{O}}_n$. This provides a quasi-classical analogue of a quantum result of Levasseur and Stafford. A detailed study of the geometry of this Hamiltonian reduction reveals that $\overline{T^*\mathbb{O}_n}^{\mathrm{aff}}$ has no symplectic resolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03421 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A connection between minimal nilpotent orbits of types A and D via Hamiltonian reduction Fu, Baohua Liu, Jie Representation Theory Algebraic Geometry 17B08, 14L30, 53D20, 16S32 We establish a novel connection between the minimal nilpotent orbit $\mathbb{O}_n$ in $\mathfrak{sl}_n$ and the minimal nilpotent orbit closure $\overline{\mathbf{O}}_n$ in $\mathfrak{so}_{2n+2}$, which differs from the shared-orbit paradigm of Brylinski and Kostant, where no direct type-A--type-D relation appears. More precisely, we show that the affine closure of the cotangent bundle $\overline{T^*\mathbb{O}_n}^{\mathrm{aff}}$ is isomorphic to a $\mathbb{C}^*$-Hamiltonian reduction of $\overline{\mathbf{O}}_n$. This provides a quasi-classical analogue of a quantum result of Levasseur and Stafford. A detailed study of the geometry of this Hamiltonian reduction reveals that $\overline{T^*\mathbb{O}_n}^{\mathrm{aff}}$ has no symplectic resolution. |
| title | A connection between minimal nilpotent orbits of types A and D via Hamiltonian reduction |
| topic | Representation Theory Algebraic Geometry 17B08, 14L30, 53D20, 16S32 |
| url | https://arxiv.org/abs/2605.03421 |