Cohomology of the hyperplane complement of a quaternionic reflection group

2025/10/21 by Griffeth, Stephen, Guevara, David
#20F55 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.18607

Abstract

We compute the graded rank of the cohomology of the hyperplane complement associated with a quaternionic reflection group, and observe that it factors into irreducible factors with positive integer coefficients. For an irreducible group, these irreducible factors are all linear except at most one irreducible quadratic factor, which occurs for precisely three of the exceptional groups.

Citations

• Invariants in the cohomology of the complement of quaternionic reflection arrangements
• Systems of imprimitivity for rank two quaternionic reflection groups
• Zero fibers of quaternionic quotient singularities
• On Parabolic Subgroups of Symplectic Reflection Groups
• The Cohomology of Quaternionic Hyperplane Complements

Related

• Invariants in the cohomology of the complement of quaternionic reflection arrangements
• The Cohomology of Quaternionic Hyperplane Complements
• Zero fibers of quaternionic quotient singularities
• An elementary classification of the quaternionic reflection groups of rank two
• Invariants and semi-invariants in the cohomology of the complement of a reflection arrangement