TY - JOUR

T1 - Recursively free reflection arrangements

AU - Mücksch, Paul

PY - 2017/3/15

Y1 - 2017/3/15

N2 - Let A=A(W) be the reflection arrangement of the finite complex reflection group $W$. By Terao's famous theorem, the arrangement A 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 G_{31} we obtain a new (computer-free) proof for the non-inductive freeness of A(W). Since our classification implies the non-recursive freeness of the reflection arrangement A(G_{31}), we can prove a conjecture by Abe about the new class of divisionally free arrangements which he recently introduced.

AB - Let A=A(W) be the reflection arrangement of the finite complex reflection group $W$. By Terao's famous theorem, the arrangement A 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 G_{31} we obtain a new (computer-free) proof for the non-inductive freeness of A(W). Since our classification implies the non-recursive freeness of the reflection arrangement A(G_{31}), we can prove a conjecture by Abe about the new class of divisionally free arrangements which he recently introduced.

KW - Divisionally free arrangements

KW - Hyperplane arrangements

KW - Inductively free arrangements

KW - Recursively free arrangements

KW - Reflection arrangements

UR - http://www.scopus.com/inward/record.url?scp=84999035155&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2016.10.041

DO - 10.1016/j.jalgebra.2016.10.041

M3 - Article

VL - 474

SP - 24

EP - 48

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 474

ER -