Reflection arrangements and ribbon representations

Details Reflection arrangements and ribbon representations Reflection arrangements and ribbon representations

2011-08-06

arxiv.org/abs/1108.1429v3

Mathematics

Combinatorics

Version 3. 34 pages. Added section on additional properties of ribbon representations. Minor edits made to the introduction

Scientific paper

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.

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