Lusztig varieties for regular elements
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916584873787392 |
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| author | He, Xuhua La, Ruben |
| author_facet | He, Xuhua La, Ruben |
| contents | Let $G$ be a connected reductive group over an algebraically closed field. Let $B$ be a Borel subgroup of $G$ and $W$ be the associated Weyl group. We show that for any $w \in W$ that is not contained in any standard parabolic subgroup of $W$, the intersection of the Bruhat cell $B w B$ with any regular conjugacy class of $G$ is always irreducible. We then prove that the associated Lusztig varieties are irreducible. This extends the previous work of Kim \cite{kim2020homology} on the regular semisimple and regular unipotent elements. The irreducibilitiy result of Lusztig varieties will be used in an upcoming work in the study of affine Lusztig varieties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_15827 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lusztig varieties for regular elements He, Xuhua La, Ruben Representation Theory Algebraic Geometry 20G07, 20F55, 20E45, 20C08 Let $G$ be a connected reductive group over an algebraically closed field. Let $B$ be a Borel subgroup of $G$ and $W$ be the associated Weyl group. We show that for any $w \in W$ that is not contained in any standard parabolic subgroup of $W$, the intersection of the Bruhat cell $B w B$ with any regular conjugacy class of $G$ is always irreducible. We then prove that the associated Lusztig varieties are irreducible. This extends the previous work of Kim \cite{kim2020homology} on the regular semisimple and regular unipotent elements. The irreducibilitiy result of Lusztig varieties will be used in an upcoming work in the study of affine Lusztig varieties. |
| title | Lusztig varieties for regular elements |
| topic | Representation Theory Algebraic Geometry 20G07, 20F55, 20E45, 20C08 |
| url | https://arxiv.org/abs/2501.15827 |