University of Sydney Algebra Seminar

Anthony Henderson (University of Sydney)

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

Braid groups of normalizers of reflection subgroups

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.