Coxeter groups, imaginary cones and dominance

Xiang Fu

Vol. 262 (2013), No. 2, 339–363

DOI: 10.2140/pjm.2013.262.339

Abstract

Brink and Howlett [Math. Ann. 296:1 (1993), 179–190] have introduced a partial ordering, called dominance, on the root systems of Coxeter groups in their proof that all finitely generated Coxeter groups are automatic. Edgar (Ph.D. thesis, 2009), in an investigation of various regularity properties of Coxeter groups, studied a function on the reflections of such groups, called ∞-height. Here we show that these two concepts are closely related to each other. We also give applications of dominance to the study of imaginary cones of Coxeter groups.

Keywords

Coxeter groups, root systems, Tits cone, dominance

Mathematical Subject Classification 2010

Primary: 20F55, 20F65

Secondary: 20F10

Milestones

Received: 26 January 2012

Revised: 19 October 2012

Accepted: 13 November 2012

Published: 16 April 2013