Thursday, 18 January 2018
Georges Neaime: Interval structures for the generalized braid groups B(e,e,n)
In 1998, M. Broué, G. Malle and R. Rouquier attached a generalized braid group to each complex reflection group. They are a generalizations of Artin-Tits groups associated to Coxeter groups.The generalized braid groups B(e,e,n) admit classical Garside structures (R. Corran and M. Picantin) and dual Garside structures (D. Bessis and R. Corran). We are interested in Garside structures that derive from intervals in the associated complex reflection groups G(e,e,n).
We define a geodesic normal form for G(e,e,n) and construct intervals that give rise to Garside groups. Some of these groups correspond to B(e,e,n). For the other Garside groups that appear, we give some of their properties in order to understand these new structures.