Parabolic Subgroups of Singular Artin Monoids

Speaker: Noelle Antony, University of Sydney

Abstract: The talk concerns parabolic submonoids of a class of monoids known as singular Artin monoids. The latter class includes the singular braid monoid -- a geometric extension of the braid group which was created for the sole purpose of studying Vassiliev invariants in knot theory. But those monoids may also be construed (and indeed, are defined) as a formal extension of Artin groups which, in turn, naturally generalise braid groups. It is the case, by H. van der Lek and L. Paris, that standard parabolic subgroups of Artin groups are canonically isomorphic to Artin groups. This would naturally invite us to consider whether the same holds for parabolic submonoids of singular Artin monoids. We show that it is in fact true when the corresponding Coxeter matrix is of "type FC"; hence generalising R. Corran's result in the "finite type" case.