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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.19645 |
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| _version_ | 1866909551937191936 |
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| author | Suzuki, Kenta |
| author_facet | Suzuki, Kenta |
| contents | Let $G$ be a reductive group with Borel $B$ and Weyl group $W$. Then $B$-double cosets in $G$ are indexed by the Weyl group, say $O(w)$ for $w\in W$. Then we prove the minimal $B$-double coset in the convolution $O(w_1)*O(w_2)$ is $O(w_1w_2)$, which gives a geometric characterization of multiplication in $W$. This defines the abstract Weyl group $\mathbf W$ which is a Coxeter group acting on the abstract Cartan $\mathbf T$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric characterization of the group law in the Weyl group Suzuki, Kenta Representation Theory Let $G$ be a reductive group with Borel $B$ and Weyl group $W$. Then $B$-double cosets in $G$ are indexed by the Weyl group, say $O(w)$ for $w\in W$. Then we prove the minimal $B$-double coset in the convolution $O(w_1)*O(w_2)$ is $O(w_1w_2)$, which gives a geometric characterization of multiplication in $W$. This defines the abstract Weyl group $\mathbf W$ which is a Coxeter group acting on the abstract Cartan $\mathbf T$. |
| title | Geometric characterization of the group law in the Weyl group |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2503.19645 |