Every affine reflection group has a Coxeter presentation (https://en.wikipedia.org/wiki/Reflection_group#Relation_with_Coxeter_groups). How do you tell which Coxeter presentations arise from affine reflection groups in this way?
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1$\begingroup$ If I am not mistaken, the Cartan matrix has to be positive semidefinit with kernel dimension 1. $\endgroup$– Sebastian GoetteCommented Dec 20, 2015 at 21:25
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7$\begingroup$ en.wikipedia.org/wiki/Coxeter_group#Affine_Coxeter_groups $\endgroup$– YCorCommented Dec 20, 2015 at 21:27
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