Journal of the Australian Mathematical Society

Research Article

Special involutions and bulky parabolic subgroups in finite Coxeter groups

Götz Pfeiffera1 and Gerhard Röhrlea2

a1 Department of Mathematics National University of Ireland Galway Ireland e-mail: goetz.pfeiffer@nuigalway.ie

a2 School of Mathematics University of Birmingham Birmingham B15 2TT United Kingdom e-mail: ger@for.mat.bham.ac.uk

Abstract

The conjugacy classes of so-called special involutions parameterize the constituents of the action of a finite Coxeter group on the cohomology of the complement of its complexified hyperplane arrangement. In this note we give a short intrinsic characterisation of special involutions in terms of so-called bulky parabolic subgroups.

(Received May 20 2004)

(Revised September 20 2004)

2000 Mathematics subject classification

  • primary 20F55;
  • secondary 06A07