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arXiv · 1008.5291

Finite Weyl groupoids

Michael Cuntz·Istvan Heckenberger
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Abstract

Using previous results concerning the rank two and rank three cases, all connected simply connected Cartan schemes for which the real roots form a finite irreducible root system of arbitrary rank are determined. As a consequence one obtains the list of all crystallographic arrangements, a large subclass of the class of simplicial hyperplane arrangements. Supposing that the rank is at least three, the classification yields Cartan schemes of type $A$ and $B$, an infinite family of series involving the types $C$ and $D$, and $74$ sporadic examples.

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Michael Cuntz, Istvan Heckenberger. 2010-08-31. Finite Weyl groupoids. https://arxiv.org/abs/1008.5291

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