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
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.