Quaternionic MUBs in H^2 and their reflection symmetries
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909765703041024 |
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| author | Buckley, Zachary Waldron, Shayne |
| author_facet | Buckley, Zachary Waldron, Shayne |
| contents | We consider the primitive quaternionic reflection groups of type P for H^2 that are obtained from Blichfeldt's collineation groups for C^4.These are seen to be intimately related to the maximal set of five quaternionic mutually unbiased bases (MUBs) in H2 , for which they are symmetries. From these groups, we construct other interesting sets of lines that they fix, including a new quaternionic spherical 3-design of 16 lines in H^2 with angles {1/5,3/5}, which meets the special bound. Some interesting consequences of this investigation include finding imprimitive quaternionic reflection groups with several systems of imprimitivity, and finding a nontrivial reducible subgroup which has a continuous family of eigenvectors. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_01859 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quaternionic MUBs in H^2 and their reflection symmetries Buckley, Zachary Waldron, Shayne Representation Theory Group Theory 05B30, 15B33, 20C25, 20F55, 20G20, 51F15 We consider the primitive quaternionic reflection groups of type P for H^2 that are obtained from Blichfeldt's collineation groups for C^4.These are seen to be intimately related to the maximal set of five quaternionic mutually unbiased bases (MUBs) in H2 , for which they are symmetries. From these groups, we construct other interesting sets of lines that they fix, including a new quaternionic spherical 3-design of 16 lines in H^2 with angles {1/5,3/5}, which meets the special bound. Some interesting consequences of this investigation include finding imprimitive quaternionic reflection groups with several systems of imprimitivity, and finding a nontrivial reducible subgroup which has a continuous family of eigenvectors. |
| title | Quaternionic MUBs in H^2 and their reflection symmetries |
| topic | Representation Theory Group Theory 05B30, 15B33, 20C25, 20F55, 20G20, 51F15 |
| url | https://arxiv.org/abs/2509.01859 |