The quaternionic systems of imprimitivity for the reflection groups of rank two
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911395643129856 |
|---|---|
| author | Waldron, Shayne |
| author_facet | Waldron, Shayne |
| contents | Given an explicit presentation of a reflection group of rank two (or any rank two group for that matter), we give a simple procedure for calculating all its systems of imprimitivity, when viewed as a matrix group over the quaternions. This is applied to all the reflection groups, in particular the quaternionic reflection groups, thereby unifying a number of results and ideas in the literature. For example, a primitive complex reflection group of rank two has either uncountably many quaternionic systems of imprimitivity (3 cases) or none (16 cases). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17075 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The quaternionic systems of imprimitivity for the reflection groups of rank two Waldron, Shayne Group Theory 15B33, 20F55, 20G20, 51F15 Given an explicit presentation of a reflection group of rank two (or any rank two group for that matter), we give a simple procedure for calculating all its systems of imprimitivity, when viewed as a matrix group over the quaternions. This is applied to all the reflection groups, in particular the quaternionic reflection groups, thereby unifying a number of results and ideas in the literature. For example, a primitive complex reflection group of rank two has either uncountably many quaternionic systems of imprimitivity (3 cases) or none (16 cases). |
| title | The quaternionic systems of imprimitivity for the reflection groups of rank two |
| topic | Group Theory 15B33, 20F55, 20G20, 51F15 |
| url | https://arxiv.org/abs/2601.17075 |