Parabolic subgroups of complex braid groups: the remaining case
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929264160407552 |
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| author | Garnier, Owen |
| author_facet | Garnier, Owen |
| contents | Recently, Marin and González-Meneses introduced a class of ``parabolic'' subgroups for generalized braid groups associated to arbitrary complex reflection groups. Using notably Garside group structures on these generalized braid groups, they proved general results on parabolic subgroups for all cases but one. This last case is that of the complex braid group B(G31), which has no Garside group structure known so far, but instead a Garside groupoid structure. Using this Garside groupoid structure, we complete the results of Marin and González-Meneses by proving their main theorems for the parabolic subgroups of the complex braid group B(G31). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02209 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parabolic subgroups of complex braid groups: the remaining case Garnier, Owen Group Theory Geometric Topology Representation Theory Primary 20F36, Secondary 20F55 Recently, Marin and González-Meneses introduced a class of ``parabolic'' subgroups for generalized braid groups associated to arbitrary complex reflection groups. Using notably Garside group structures on these generalized braid groups, they proved general results on parabolic subgroups for all cases but one. This last case is that of the complex braid group B(G31), which has no Garside group structure known so far, but instead a Garside groupoid structure. Using this Garside groupoid structure, we complete the results of Marin and González-Meneses by proving their main theorems for the parabolic subgroups of the complex braid group B(G31). |
| title | Parabolic subgroups of complex braid groups: the remaining case |
| topic | Group Theory Geometric Topology Representation Theory Primary 20F36, Secondary 20F55 |
| url | https://arxiv.org/abs/2403.02209 |