An inductive approach to Coxeter arrangements and Solomon%26apos;s descent algebra

作者：Douglass J Matthew; Pfeiffer Goetz; Roehrle Gerhard

来源：Journal of Algebraic Combinatorics, 2012, 35(2): 215-235.

DOI：10.1007/s10801-011-0301-9

• Coxeter groups
• Reflection arrangements
• Descent algebra
• Dihedral groups

In our recent paper (Douglass et al. arXiv: 1101.2075 (2011)), we claimed that both the group algebra of a finite Coxeter group W as well as the Orlik-Solomon algebra of W can be decomposed into a sum of induced one-dimensional representations of centralizers, one for each conjugacy class of elements of W, and gave a uniform proof of this claim for symmetric groups. In this note, we outline an inductive approach to our conjecture. As an application of this method, we prove the inductive version of the conjecture for finite Coxeter groups of rank up to 2.

• 出版日期2012-3