Title: Interval groups related to finite Coxeter groups I
Abstract:We derive presentations of the interval groups related to all quasi-Coxeter elements in the Coxeter group of type D n . Type D n is the only infinite family of finite Coxeter groups that admits proper...We derive presentations of the interval groups related to all quasi-Coxeter elements in the Coxeter group of type D n . Type D n is the only infinite family of finite Coxeter groups that admits proper quasi-Coxeter elements. The presentations we obtain are over a set of generators in bijection with what we call a Carter generating set, and the relations are those defined by the related Carter diagram together with a twisted cycle or a cycle commutator relator, depending on whether the quasi-Coxeter element is a Coxeter element or not. The proof is based on the description of two combinatorial techniques related to the intervals of quasi-Coxeter elements.Read More