Weyl-invariant subspaces are (usually) not generic
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916990581473280 |
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| author | Kurama, Riku Li, Ruoxi Talbott, Henry Webb, Rachel |
| author_facet | Kurama, Riku Li, Ruoxi Talbott, Henry Webb, Rachel |
| contents | Let $V$ be a linear representation of a connected complex reductive group $G$. Given a choice of character $θ$ of $G$, Geometric Invariant Theory defines a locus $V^{ss}_θ(G) \subseteq V$ of semistable points. We give necessary, sufficient, and in some cases equivalent conditions for the existence of $θ$ such that a maximal torus $T$ of $G$ acts on $V^{ss}_θ(T)$ with finite stabilizers. In such cases, the stack quotient $[V^{ss}_θ(G)/G]$ is is known to be Deligne-Mumford. Our proof uses the combinatorial structure of the weights of irreducible representations of semisimple groups. As an application we generalize the Grassmannian flop example of Donovan-Segal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03963 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weyl-invariant subspaces are (usually) not generic Kurama, Riku Li, Ruoxi Talbott, Henry Webb, Rachel Representation Theory Let $V$ be a linear representation of a connected complex reductive group $G$. Given a choice of character $θ$ of $G$, Geometric Invariant Theory defines a locus $V^{ss}_θ(G) \subseteq V$ of semistable points. We give necessary, sufficient, and in some cases equivalent conditions for the existence of $θ$ such that a maximal torus $T$ of $G$ acts on $V^{ss}_θ(T)$ with finite stabilizers. In such cases, the stack quotient $[V^{ss}_θ(G)/G]$ is is known to be Deligne-Mumford. Our proof uses the combinatorial structure of the weights of irreducible representations of semisimple groups. As an application we generalize the Grassmannian flop example of Donovan-Segal. |
| title | Weyl-invariant subspaces are (usually) not generic |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2510.03963 |