Systems of imprimitivity for rank two quaternionic reflection groups

2025/10/25 by Donald E Taylor, Taylor, Donald E · 2 citations
Mathematics · #20D25 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20D25 #msc:20F55 #msc:51F15

paper · pdf · doi:10.48550/arxiv.2510.22134

21 pages. Corrections to Tables 1 and 5. Added references and acknowledgements. Corrected a few typos. Added Remarks

arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

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.

Citations

• An elementary classification of the quaternionic reflection groups of rank two
• On Parabolic Subgroups of Symplectic Reflection Groups
• On smoothness of minimal models of quotient singularities by finite subgroups of SL_n(ℂ)

Cited by

• Namikawa--Weyl groups of symplectic quotient singularities
• Invariants in the cohomology of the complement of quaternionic reflection arrangements
• Cohomology of the hyperplane complement of a quaternionic reflection group

Related

• An elementary classification of the quaternionic reflection groups of rank two
• Quaternionic MUBs in H² and their reflection symmetries
• Computing arithmetic invariants for hyperbolic reflection groups
• Reflection Groups. A Contribution to the Handbook of Algebra
• On Rank 2 Complex Reflection Groups