On rank 2 complex reflection groups

Pramod N. Achar, Louisiana State University
Anne Marie Aubert, Institut de Mathématiques de Jussieu-Paris Rive Gauche


We describe a class of groups with the property that the finite ones among them are precisely the complex reflection groups of rank 2. This situation is reminiscent of Coxeter groups, among which the finite ones are precisely the real reflection groups. We also study braid relations between complex reflections and indicate connections to an axiomatic study of root systems and to the Shephard-Todd "collineation groups". Copyright © Taylor & Francis Group, LLC.