Lagrangian subvarieties of hyperspherical varieties related to $G_2$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915264505839616 |
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| author | Kononenko, Nikolay |
| author_facet | Kononenko, Nikolay |
| contents | We consider two $S$-dual hyperspherical varieties of the group $G_2 \times \text{SL}(2)$: an equivariant slice for $G_2$, and the symplectic representation of $G_2 \times \text{SL}_2$ in the odd part of the basic classical Lie superalgebra $\mathfrak{g}(3)$. For these varieties we check the equality of numbers of irreducible components of their Lagrangian subvarieties (zero levels of the moment maps of Borel subgroups' actions) conjectured in arXiv:2310.19770. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19033 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lagrangian subvarieties of hyperspherical varieties related to $G_2$ Kononenko, Nikolay Algebraic Geometry Representation Theory 14J42, 53D20, 53D37 We consider two $S$-dual hyperspherical varieties of the group $G_2 \times \text{SL}(2)$: an equivariant slice for $G_2$, and the symplectic representation of $G_2 \times \text{SL}_2$ in the odd part of the basic classical Lie superalgebra $\mathfrak{g}(3)$. For these varieties we check the equality of numbers of irreducible components of their Lagrangian subvarieties (zero levels of the moment maps of Borel subgroups' actions) conjectured in arXiv:2310.19770. |
| title | Lagrangian subvarieties of hyperspherical varieties related to $G_2$ |
| topic | Algebraic Geometry Representation Theory 14J42, 53D20, 53D37 |
| url | https://arxiv.org/abs/2404.19033 |