Presentations of the braid group of the complex reflection group $G(d,d,n)$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912159823298560 |
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| author | Fedele, Francesca Marsh, Bethany Rose |
| author_facet | Fedele, Francesca Marsh, Bethany Rose |
| contents | We show that the braid group associated to the complex reflection group $G(d,d,n)$ is an index $d$ subgroup of the braid group of the orbifold quotient of the complex numbers by a cyclic group of order $d$. We also give a compatible presentation of $G(d,d,n)$ and its braid group for each tagged triangulation of the disk with $n$ marked points on its boundary and an interior marked point (interpreted as a cone point of degree $d$) in such a way that the presentations of Broué-Malle-Rouquier correspond to a special tagged triangulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12802 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Presentations of the braid group of the complex reflection group $G(d,d,n)$ Fedele, Francesca Marsh, Bethany Rose Representation Theory Algebraic Topology Combinatorics Group Theory Geometric Topology primary 20F36, 20F55, 57M05, secondary 05E10, 13F60 We show that the braid group associated to the complex reflection group $G(d,d,n)$ is an index $d$ subgroup of the braid group of the orbifold quotient of the complex numbers by a cyclic group of order $d$. We also give a compatible presentation of $G(d,d,n)$ and its braid group for each tagged triangulation of the disk with $n$ marked points on its boundary and an interior marked point (interpreted as a cone point of degree $d$) in such a way that the presentations of Broué-Malle-Rouquier correspond to a special tagged triangulation. |
| title | Presentations of the braid group of the complex reflection group $G(d,d,n)$ |
| topic | Representation Theory Algebraic Topology Combinatorics Group Theory Geometric Topology primary 20F36, 20F55, 57M05, secondary 05E10, 13F60 |
| url | https://arxiv.org/abs/2412.12802 |