Topology of eigenspace posets for unitary reflection groups

Justin Koonin

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.

Keywords: Poset topology, unitary reflection groups, Cohen-Macaulay, subspace arrangement.

AMS Subject Classification: Primary 20F55; secondary 05E45.