4 papers
The lattice of normal reflection subgroups of an irreducible reflection group
Shayne Waldron
The reflection subgroups of a reflection group have a natural lattice structure given by the reflections that they contain. By considering the conjugation action orbits of the refl…
The quaternionic systems of imprimitivity for the reflection groups of rank two
Shayne Waldron
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 imprimitivit…
Quaternionic MUBs in H^2 and their reflection symmetries
Zachary Buckley, Shayne Waldron
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 t…
The geometry of the six quaternionic equiangular lines in
Shayne Waldron
We give a simple presentation of the six quaternionic equiangular lines in as an orbit of the primitive quaternionic reflection group of order 720 (which is isomorph…