Extended Affine Weyl Groups: Presentation by Conjugation via Integral Collection

Abstract

We give several necessary and sufficient conditions for the existence of the presentation by conjugation for a non-simply laced extended affine Weyl group. We invent a computational tool by which one can determine simply the existence of the presentation by conjugation for an extended affine Weyl group. As an application, we determine the existence of the presentation by conjugation for a large class of extended affine Weyl groups.

Key Words:

• Coxeter group
• Extended affine root system
• Extended affine Weyl group
• Presentation by conjugation

2000 Mathematics Subject Classification:

• 17B67
• 17B65
• 20F55
• 22E65
• 22E40

ACKNOWLEDGMENT

The authors would like to thank the Center of Excellence for Mathematics, University of Isfahan. This research was in part supported by a grant from IPM, (No. 89170216).

Notes

Communicated by A. Elduque.