On the affinization of a nilpotent orbit cover
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866917841605754880 |
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| author | Matvieievskyi, Dmytro |
| author_facet | Matvieievskyi, Dmytro |
| contents | Let $\mathfrak{g}$ be a simple classical Lie algebra over $\mathbb{C}$ and $G$ be the adjoint group. Consider a nilpotent element $e\in \mathfrak{g}$, and the adjoint orbit $\mathbb{O}=Ge$. The formal slices to the codimension $2$ orbits in the closure $\overline{\mathbb{O}}\subset \mathfrak{g}$ are well-known due to the work of Kraft and Procesi. In this paper, we prove a similar result for the universal $G$-equivariant cover $\widetilde{\mathbb{O}}$ of $\mathbb{O}$. Namely, we describe the codimension $2$ singularities for its affinization $Spec(\mathbb{C}[\widetilde{\mathbb{O}}])$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_09356 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the affinization of a nilpotent orbit cover Matvieievskyi, Dmytro Representation Theory Let $\mathfrak{g}$ be a simple classical Lie algebra over $\mathbb{C}$ and $G$ be the adjoint group. Consider a nilpotent element $e\in \mathfrak{g}$, and the adjoint orbit $\mathbb{O}=Ge$. The formal slices to the codimension $2$ orbits in the closure $\overline{\mathbb{O}}\subset \mathfrak{g}$ are well-known due to the work of Kraft and Procesi. In this paper, we prove a similar result for the universal $G$-equivariant cover $\widetilde{\mathbb{O}}$ of $\mathbb{O}$. Namely, we describe the codimension $2$ singularities for its affinization $Spec(\mathbb{C}[\widetilde{\mathbb{O}}])$. |
| title | On the affinization of a nilpotent orbit cover |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2003.09356 |