Reflection arrangements are hereditarily free
Torsten Hoge, Gerhard Roehrle
TL;DR
This paper confirms the conjecture that all restrictions of reflection arrangements from finite reflection groups are free, completing the classification of hereditarily free arrangements.
Contribution
It proves that all restrictions of reflection arrangements are free, settling the longstanding conjecture by Orlik and Terao.
Findings
Confirmed the conjecture for all remaining cases
Established that restrictions of reflection arrangements are hereditarily free
Contributed to the classification of free hyperplane arrangements
Abstract
Suppose that W is a finite, unitary, reflection group acting on the complex vector space V. Let A = A(W) be the associated hyperplane arrangement of W. Terao has shown that each such reflection arrangement A is free. Let L(A) be the intersection lattice of A. For a subspace X in L(A) we have the restricted arrangement A^X in X by means of restricting hyperplanes from A to X. In 1992, Orlik and Terao conjectured that each such restriction is again free. In this note we settle the outstanding cases confirming the conjecture.
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