Reflection arrangements are hereditarily free
Copyright policy )Reflection arrangements are hereditarily free
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.
6 pages; to appear in Tohoku Math. J
- Ruhr University Bochum Germany
Configurations and arrangements of linear subspaces, 20F55, 52B30, 52C35, 14N20, Complex reflection groups, Freeness of restrictions of reflection arrangements, Reflection groups, reflection geometries, 52B30, Group Theory (math.GR), Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Derivations and commutative rings, complex reflection groups, 52C35, Reflection and Coxeter groups (group-theoretic aspects), FOS: Mathematics, freeness of restrictions of reflection arrangements, 14N20, 20F55, Mathematics - Group Theory, 13N15
Configurations and arrangements of linear subspaces, 20F55, 52B30, 52C35, 14N20, Complex reflection groups, Freeness of restrictions of reflection arrangements, Reflection groups, reflection geometries, 52B30, Group Theory (math.GR), Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Derivations and commutative rings, complex reflection groups, 52C35, Reflection and Coxeter groups (group-theoretic aspects), FOS: Mathematics, freeness of restrictions of reflection arrangements, 14N20, 20F55, Mathematics - Group Theory, 13N15
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