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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.01530 |
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| _version_ | 1866915682868789248 |
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| author | Voloshyn, Dmitriy |
| author_facet | Voloshyn, Dmitriy |
| contents | We study the decomposition of a generic element $g \in G$ of a connected reductive complex algebraic group $G$ in the form $g = N(g) B(g) \bar{u} N(g)^{-1}$ where $N: G \dashrightarrow \mathcal{N}_-$ and $B : G \dashrightarrow \mathcal{B}_+$ are rational maps onto a unipotent subgroup $\mathcal{N}_-$ and a Borel subgroup $\mathcal{B}_+$ opposite to $\mathcal{N}_-$, and $\bar{u}$ is a representative of a Weyl group element $u$. We introduce a class of rational Weyl group elements that give rise to such decompositions, and study their various properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01530 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiple rational normal forms in Lie theory Voloshyn, Dmitriy Representation Theory 20G07 (Primary) 20F55, 13F60 (Secondary) We study the decomposition of a generic element $g \in G$ of a connected reductive complex algebraic group $G$ in the form $g = N(g) B(g) \bar{u} N(g)^{-1}$ where $N: G \dashrightarrow \mathcal{N}_-$ and $B : G \dashrightarrow \mathcal{B}_+$ are rational maps onto a unipotent subgroup $\mathcal{N}_-$ and a Borel subgroup $\mathcal{B}_+$ opposite to $\mathcal{N}_-$, and $\bar{u}$ is a representative of a Weyl group element $u$. We introduce a class of rational Weyl group elements that give rise to such decompositions, and study their various properties. |
| title | Multiple rational normal forms in Lie theory |
| topic | Representation Theory 20G07 (Primary) 20F55, 13F60 (Secondary) |
| url | https://arxiv.org/abs/2506.01530 |