Finite Weyl groupoids

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 subc...

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Bibliographic Details
Published in:Journal für die reine und angewandte Mathematik 2015-05, Vol.2015 (702), p.77-108
Main Authors: Cuntz, Michael, Heckenberger, István
Format: Article
Language:English
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Summary: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 and , an infinite family of series involving the types and , and 74 sporadic examples.
ISSN:0075-4102
1435-5345
DOI:10.1515/crelle-2013-0033