Parabolic Normalizers in Finite Coxeter Groups as Subdirect Products

J. Matthew Douglass, Götz Pfeiffer, Gerhard Roehrle

We revisit the structure of the normalizer $N_W(P)$ of a parabolic subgroup $P$ in a finite Coxeter group $W$, originally described by Howlett. Building on Howlett's Lemma, which p…