Projective reflection groups

TL;DR

This paper introduces projective reflection groups, a new class encompassing all complex reflection groups, and demonstrates their relevance in understanding combinatorics and representation theory of these groups.

Contribution

It defines the class of projective reflection groups and shows their applicability to the combinatorics and representation theory of complex reflection groups.

Findings

Includes all complex reflection groups within the new class

Provides natural descriptions for combinatorics of non-exceptional groups

Offers insights into the representation theory of these groups

Abstract

We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all non exceptional irreducible complex reflection groups find a natural description in this wider setting.