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math.GR2026
On Normalizers of Parabolic Subgroups of Quaternionic Reflection Groups
Gerhard Roehrle, Johannes Schmitt
By work of Howlett and Muraleedaran--Taylor, a parabolic subgroup of a real or complex reflection group always admits a complement in its normalizer. In this note, we investigate t…
math.GR2026
Parabolic Normalizers in Finite Coxeter Groups as Subdirect Products
J. Matthew Douglass, Götz Pfeiffer, Gerhard Roehrle
We revisit the structure of the normalizer of a parabolic subgroup in a finite Coxeter group , originally described by Howlett. Building on Howlett's Lemma, which p…