Isomorphism and non-isomorphism for interval groups of type Dn

Barbara Baumeister, Derek Holt, George Neaime and Sarah Rees

Keywords

Coxeter groups, Quasi-Coxeter elements, Carter diagrams, Artin(--Tits) groups, dual approach to Coxeter and Artin groups, generalised non-crossing partitions, Garside structures, Interval (Garside) structures.

Status

Submitted for publication

Abstract

We consider the interval groups associated with proper quasi-Coxeter elements of the Coxeter group W(Dn), for which presentations were derived in an article of Baumeister, Neaime and Rees. We derive alternative presentations for the groups, and use these to show that the interval group associated with a proper quasi-Coxeter element of W(Dn) cannot be isomorphic to the Artin group of type Dn.


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