Classifications of pseudo-reflection groups

Abstract

In this chapter, we sketch some of the classification results obtained for pseudo-reflection groups in the nonmodular case. The classification results given in this chapter are not used elsewhere, and are simply given as illustrations of the type of patterns that hold. We begin by sketching the Shephard-Todd classification of the finite complex pseudo-reflection groups. We then explain how this classification can be used to obtain classifications of pseudo-reflection groups over other fields. The Shephard-Todd classification is the key to all other classifications described in this chapter. We shall omit most details, and only sketch arguments.