Fully commutative elements of the complex reflection groups

Abstract

We extend the usual notion of fully commutative elements from the finite Coxeter groups to the complex reflection groups. We decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties, and investigate the structure of these decompositions. As a consequence, we enumerate and describe the form of these elements for the complex reflection groups. © 2019 Elsevier Inc.