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arXiv · 2509.01859

Quaternionic MUBs in H^2 and their reflection symmetries

Zachary Buckley·Shayne Waldron
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Abstract

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.

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Zachary Buckley, Shayne Waldron. 2025-09-02. Quaternionic MUBs in H^2 and their reflection symmetries. https://arxiv.org/abs/2509.01859

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