Reflection arrangements and ribbon representations
Combinatorics
2011-11-17 v3 Group Theory
Geometric Topology
Representation Theory
Abstract
Ehrenborg and Jung recently related the order complex for the lattice of d-divisible partitions with the simplicial complex of pointed ordered set partitions via a homotopy equivalence. The latter has top homology naturally identified as a Specht module. Their work unifies that of Calderbank, Hanlon, Robinson, and Wachs. By focusing on the underlying geometry, we strengthen and extend these results from type A to all real reflection groups and the complex reflection groups known as Shephard groups.
Cite
@article{arxiv.1108.1429,
title = {Reflection arrangements and ribbon representations},
author = {Alexander Miller},
journal= {arXiv preprint arXiv:1108.1429},
year = {2011}
}
Comments
Version 3. 34 pages. Added section on additional properties of ribbon representations. Minor edits made to the introduction