(The) structure of automorphism groups of CLTTF Artin groups

Abstract

We obtain a presentation of the automorphism group of a CLTTF Artin group. In fact, it is generated by inversions, partial conjugations, graph automorphisms, and partial reflections. The complication due to the non-uniqueness of defining graphs is managed by surprisingly simple automorphisms called partial reflections. Relations are basically given by conjugation actions of one type of automorphisms to the other.