Reflection arrangements are hereditarily free
classification
🧮 math.GR
math.AC
keywords
arrangementfreereflectionteraoactingarrangementsassociatedcases
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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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