Lagrangian subvarieties of hyperspherical varieties
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916654023180288 |
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| author | Finkelberg, Michael Ginzburg, Victor Travkin, Roman |
| author_facet | Finkelberg, Michael Ginzburg, Victor Travkin, Roman |
| contents | Given a hyperspherical $G$-variety $\mathscr X$ we consider the zero moment level $Λ_{\mathscr X}\subset{\mathscr X}$ of the action of a Borel subgroup $B\subset G$. We conjecture that $Λ_{\mathscr X}$ is Lagrangian. For the dual $G^\vee$-variety ${\mathscr X}^\vee$, we conjecture that that there is a bijection between the sets of irreducible components $\mathrm{Irr}Λ_{\mathscr X}$ and $\mathrm{Irr}Λ_{{\mathscr X}^\vee}$. We check this conjecture for all the hyperspherical equivariant slices, and for all the basic classical Lie superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19770 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lagrangian subvarieties of hyperspherical varieties Finkelberg, Michael Ginzburg, Victor Travkin, Roman Algebraic Geometry Representation Theory Symplectic Geometry Given a hyperspherical $G$-variety $\mathscr X$ we consider the zero moment level $Λ_{\mathscr X}\subset{\mathscr X}$ of the action of a Borel subgroup $B\subset G$. We conjecture that $Λ_{\mathscr X}$ is Lagrangian. For the dual $G^\vee$-variety ${\mathscr X}^\vee$, we conjecture that that there is a bijection between the sets of irreducible components $\mathrm{Irr}Λ_{\mathscr X}$ and $\mathrm{Irr}Λ_{{\mathscr X}^\vee}$. We check this conjecture for all the hyperspherical equivariant slices, and for all the basic classical Lie superalgebras. |
| title | Lagrangian subvarieties of hyperspherical varieties |
| topic | Algebraic Geometry Representation Theory Symplectic Geometry |
| url | https://arxiv.org/abs/2310.19770 |