On inductively free reflection arrangements
نویسندگان
چکیده
منابع مشابه
Nice Reflection Arrangements
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 > 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 th...
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In 1994, Edelman and Reiner characterized free and supersolvable hyperplane arrangements in the restricted interval [An−1, Bn]. In this paper, we give a characterization of inductively factored arrangements in this interval, and show that the same characterization also describes factored arrangements in this interval. These results use the compact notation of signed graphs introduced by Zaslavsky.
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Let V be a finite dimensional complex vector space and W ⊂ GL(V ) be a finite complex reflection group. Let V reg be the complement in V of the reflecting hyperplanes. A classical conjecture predicts that V reg is a K(π, 1) space. When W is a complexified real reflection group, the conjecture follows from a theorem of Deligne, [20]. Our main result validates the conjecture for duality (or, equi...
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The lattice of intersections of reflecting hyperplanes of a complex reflection group W may be considered as the poset of 1-eigenspaces of the elements of W . In this paper we replace 1 with an arbitrary eigenvalue and study the topology and homology representation of the resulting poset. After posing the main question of whether this poset is shellable, we show that all its upper intervals are ...
متن کاملNice Restrictions of Reflection Arrangements
In [5], Hoge and the second author classified all nice and all inductively factored reflection arrangements. In this note we extend this classification by determining all nice and all inductively factored restrictions of reflection arrangements.
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2013
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle-2013-0022