arXiv subjects

Justin Koonin

Publications and source records attributed to Justin Koonin.

3 recordsLinked to original sources

arXiv2013

Topology of eigenspace posets for unitary reflection groups

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.

math.CO↗

arXiv2013

Topology of eigenspace posets for imprimitive reflection groups

This paper studies the poset of eigenspaces of elements of an imprimitive unitary reflection group, for a fixed eigenvalue, ordered by the reverse of inclusion. The study of this poset is suggested by the eigenspace theory of Springer and Lehrer. The posets are shown to be isomorphic to certain subposets of Dowling lattices (the `d-divisible, k-evenly coloured Dowling lattices'). This enables us to prove that these posets are Cohen-Macaulay, and to determine the dimension of their top homology.

math.CO↗

arXiv2013

Homology representations of unitary reflection groups

This paper continues the study of the poset of eigenspaces of elements of a unitary reflection group (for a fixed eigenvalue), which was commenced in [6] and [5]. The emphasis in this paper is on the representation theory of unitary reflection groups. The main tool is the theory of poset extensions due to Segev and Webb ([16]). The new results place the well-known representations of unitary reflection groups on the top homology of the lattice of intersections of hyperplanes into a natural family, parameterised by eigenvalue.

math.RT↗