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

David Bessis·Ruth Corran
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Abstract

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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David Bessis, Ruth Corran. 2003-06-11. Garside structure for the braid group of G(e,e,r). https://arxiv.org/abs/math/0306186

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