Garside structure for the braid group of G(e,e,r)

Details Garside structure for the braid group of G(e,e,r) Garside structure for the braid group of G(e,e,r)

2003-06-11

arxiv.org/abs/math/0306186v1

Mathematics

Group Theory

24 pages

Scientific paper

We give a new presentation of the braid group $B$ of the complex reflection group $G(e,e,r)$ which is positive and homogeneous, and for which the generators map to reflections in the corresponding complex reflection group. We show that this presentation gives rise to a Garside structure for $B$ with Garside element a kind of generalised Coxeter element, and hence obtain solutions to the word and conjugacy problems for $B$.

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