- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:11
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
18
2016
6
The freeness of ideal subarrangements of Weyl arrangements
Takuro
Abe
Kyushu University, FUKUOKA, JAPAN
Mohamed
Barakat
Universität Siegen, SIEGEN, GERMANY
Michael
Cuntz
Leibniz Universität Hannover, HANNOVER, GERMANY
Torsten
Hoge
Leibniz Universität Hannover, HANNOVER, GERMANY
Hiroaki
Terao
Hokkaido University, SAPPORO, JAPAN
Arrangement of hyperplanes, root system,Weyl arrangement, free arrangement, ideals, dual partition theorem
A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any ideal subarrangement is a free arrangement and that its exponents are given by the dual partition of the height distribution, which was conjectured by Sommers–Tymoczko. In particular, when an ideal subarrangement is equal to the entireWeyl arrangement, our main theorem yields the celebrated formula by Shapiro, Steinberg, Kostant, and Macdonald. The proof of the main theorem is classification-free. It heavily depends on the theory of free arrangements and thus greatly differs from the earlier proofs of the formula
Several complex variables and analytic spaces
Combinatorics
Nonassociative rings and algebras
1339
1348
10.4171/JEMS/615
http://www.ems-ph.org/doi/10.4171/JEMS/615