Algebra Seminar: Henderson -- Henderson: Braid groups of normalizers of reflection subgroups

Anthony Henderson (University of Sydney) 

Friday 29 November, 12-1pm, Place: Carslaw 375 

Title: Braid groups of normalizers of reflection subgroups 

Abstract: Various results are known about the normalizers of reflection subgroups in a
complex reflection group.  At the most basic level, in certain situations it is known
that the normalizer is a semidirect product of the reflection subgroup and a
complementary subgroup.  Ivan Marin gave a topological definition of a group which
should be thought of as the braid group of such a normalizer, and raised the question of
whether it has a similar semidirect product decomposition.  In joint work with Thomas
Gobet and Ivan Marin, we show that this holds in the Coxeter case but not in general.
One corollary is a standard basis for the Hecke algebra associated to the normalizer of
a standard parabolic subgroup in a finite Coxeter group.