On reflection subgroups of finite Coxeter groups
Douglass, J. Matthew
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Douglass, J. Matthew, Pfeiffer, Götz, & Röhrle, Gerhard. (2013). On Reflection Subgroups of Finite Coxeter Groups. Communications in Algebra, 41(7), 2574-2592. doi: 10.1080/00927872.2012.661005
Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its Coxeter elements to be injective, up to conjugacy.