Topology of eigenspace posets for unitary reflection groups

TL;DR

This paper studies the topological structure of eigenspace posets in unitary reflection groups, extending classical results on hyperplane intersection lattices to a broader eigenspace context.

Contribution

It introduces new topological insights into eigenspace posets for unitary reflection groups, generalizing the work of Orlik and Solomon.

Findings

Eigenspace posets exhibit specific topological properties.

Extension of hyperplane intersection lattice results to eigenspaces.

New connections between group theory and topology in reflection groups.

Abstract

The eigenspace theory of unitary reflection groups, initiated by Springer and Lehrer, suggests that the following object is worthy of study: the poset of eigenspaces of elements of a unitary reflection group, for a fixed eigenvalue, ordered by the reverse of inclusion. We investigate topological properties of this poset. The new results extend the well-known work of Orlik and Solomon on the lattice of intersections of hyperplanes.