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

الأصل · EN

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.