Admissible Diagrams for 𝐺(𝑚, 1, 𝑛)

Abstract

In this paper, we show that every conjugacy class of the imprimitive complex reflection group 𝐺(𝑚, 1, 𝑛) can be represented by an admissible diagram. For this, we introduce a length function for elements of 𝐺(𝑚, 1, 𝑛) and study its properties. This then allows us to establish the admissible diagram for each conjugacy class of 𝐺(𝑚, 1, 𝑛). The corresponding results for Weyl groups and their conjugacy classes are well known.