Algebra Seminar

Which braids have symmetries? This seemingly strange question leads to interesting developments (which historically preceded the question). A non-trivial result is that braids which are homotopic to their symmetric have symmetric representatives. The proof involves regular elements in reflection groups (in the sense of Springer) and the Birman-Ko-Lee monoid. The same question can be more generally asked about braid groups of complex reflection groups. It can be solved in the real case by using the dual braid monoid of David Bessis.