Systems of imprimitivity for rank two quaternionic reflection groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908611761930240 |
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| author | Taylor, Donald E |
| author_facet | Taylor, Donald E |
| contents | We revise the enumeration of the imprimitive rank two quaternionic reflection groups, adding missing groups and establishing isomorphisms between groups in the published tables. The isomorphisms are obtained as a consequence of the determination of the reflection groups with more than one system of imprimitivity. We find that there are primitive complex reflection groups which have infinitely many systems of imprimitivity when represented as quaternionic reflection groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22134 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Systems of imprimitivity for rank two quaternionic reflection groups Taylor, Donald E Group Theory 20D25 We revise the enumeration of the imprimitive rank two quaternionic reflection groups, adding missing groups and establishing isomorphisms between groups in the published tables. The isomorphisms are obtained as a consequence of the determination of the reflection groups with more than one system of imprimitivity. We find that there are primitive complex reflection groups which have infinitely many systems of imprimitivity when represented as quaternionic reflection groups. |
| title | Systems of imprimitivity for rank two quaternionic reflection groups |
| topic | Group Theory 20D25 |
| url | https://arxiv.org/abs/2510.22134 |