Geodesic
Nice reflection arrangements.
Torsten Hoge1 ; Gerhard Röhrle2
1Leibniz Universität Hannover
2Ruhr-Universität Bochum
The electronic journal of combinatorics, Tome 23 (2016) no. 2
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The aim of this note is a classification of all nice and all inductively factored reflection arrangements. It turns out that apart from the supersolvable instances only the monomial groups $G(r,r,3)$ for $r \ge 3$ give rise to nice reflection arrangements. As a consequence of this and of the classification of all inductively free reflection arrangements from Hoge and Röhrle (2015) we deduce that the class of all inductively factored reflection arrangements coincides with the class of all supersolvable reflection arrangements. Moreover, we extend these classifications to hereditarily factored and hereditarily inductively factored reflection arrangements.
DOI : 10.37236/5331
Classification : 20F55, 52C35, 14N20
Mots-clés : complex reflection groups, nice reflection arrangements, inductively factored arrangements

Torsten Hoge  1   ; Gerhard Röhrle  2

1 Leibniz Universität Hannover
2 Ruhr-Universität Bochum 
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Torsten Hoge; Gerhard Röhrle. Nice reflection arrangements.. The electronic journal of combinatorics, Tome 23 (2016) no. 2. doi: 10.37236/5331

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