Abstract
The purpose of this note is to give a self-contained (apart from simple facts about Coxeter groups) and we hope a bit shorter and more understandable account of some results of [C1,C2] on normal forms of braids which are themselves based on the papers [D1,T]. In particular a motivation was to give a proof of Proposition 5.1 that we use in [B-M]. Some proofs and results from Section 2 onwards seem to be new. I thank several people for improvements from earlier versions of the manuscript: M. Geck for pointing out some errors, F. Digne for pointing out that some results don't need the braid group to be of finite type, and J.-Y. Hée for suggesting (and providing) further improvements in that direction.
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