Recursively free reflection arrangements

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• 作者：Paul Mü ; cksch ^{muecksch@math.uni-hannover.de}
• 关键词：Hyperplane arrangements ; Reflection arrangements ; Recursively free arrangements ; Inductively free arrangements ; Divisionally free arrangements
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：474
• 期：Complete
• 页码：24-48
• 全文大小：517 K
• 卷排序：474

文摘

Let A=A(W)A=A(W) be the reflection arrangement of the finite complex reflection group W  . By Terao's famous theorem, the arrangement AA is free. In this paper we classify all reflection arrangements which belong to the smaller class of recursively free arrangements. Moreover for the case that W   admits an irreducible factor isomorphic to G31G31 we obtain a new (computer-free) proof for the non-inductive freeness of A(W)A(W). Since our classification implies the non-recursive freeness of the reflection arrangement A(G31)A(G31), we can prove a conjecture by Abe about the new class of divisionally free arrangements which he recently introduced.