The freeness of ideal subarrangements of Weyl arrangements

Takuro Abe, Mohamed Barakat, Michael Cuntz, Torsten Hoge, Hiroaki Terao

研究成果: Contribution to journalArticle査読

17 被引用数 (Scopus)

抄録

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 entire Weyl 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.

本文言語英語
ページ(範囲)1339-1348
ページ数10
ジャーナルJournal of the European Mathematical Society
18
6
DOI
出版ステータス出版済み - 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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