An elementary classification of the quaternionic reflection groups of rank two
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914017139752960 |
|---|---|
| author | Waldron, Shayne |
| author_facet | Waldron, Shayne |
| contents | We give an elementary classification and presentation of the finite quaternionic reflection groups of rank two, based on the notion of a``reflection system''. This simplifies the existing classification, which is shown to be incomplete, e.g., there exist four imprimitive quaternionic reflection groups of order 192 with 22 reflections which are not isomorphic (one of which was previously unknown). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An elementary classification of the quaternionic reflection groups of rank two Waldron, Shayne Group Theory Representation Theory 05B30, 15B33, 20C25, 20G20, 51M05, 51M20 51M20 We give an elementary classification and presentation of the finite quaternionic reflection groups of rank two, based on the notion of a``reflection system''. This simplifies the existing classification, which is shown to be incomplete, e.g., there exist four imprimitive quaternionic reflection groups of order 192 with 22 reflections which are not isomorphic (one of which was previously unknown). |
| title | An elementary classification of the quaternionic reflection groups of rank two |
| topic | Group Theory Representation Theory 05B30, 15B33, 20C25, 20G20, 51M05, 51M20 51M20 |
| url | https://arxiv.org/abs/2509.01849 |