Double Centralizers of Parabolic Subgroups of Braid Groups

Abstract

We characterize the double centralizer of all parabolic subgroups of the braid groups. We apply this result to provide a new and potentially more efficient solution to the subgroup conjugacy problem for parabolic subgroups. In the course of the proof we also characterize the centralizer for all parabolic subgroups.

19 pages, 7 figures. Added Remark 3.4. Shortened abstract