Seminar of Algebra

Springer's theory of regular elements in complex reflection groups is well-known and gives several remarkable results and profound links between these groups. The existence of a "lift" of this theory in complex braid groups has been the subject of several conjectures.

In this talk I will present the notion of regular braids, which appear naturally as roots of a particular element of the pure braid group (the so-called full-twist). These elements were studied by David Bessis in the case of well-generated groups. He obtained a remarkable theorem on these elements, which provides a wonderful analogue of Springer's theory in complex braid groups.

I will present a generalization of this theorem to all irreducible complex braid groups. And some consequences on roots of central elements in irreducible braid groups (so called-periodic elements), which mimic the case of the classical braid group.