A vanishing theorem for hyperplane cohomology
- 1 June 1996
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 53 (3) , 361-368
- https://doi.org/10.1017/s0004972700017111
Abstract
Let A be a hyperplane arrangement in an arbitrary finite dimensional vector space V and let G ≤ GL(V) be an automorphism group of A. If λ is a complex representation of G such that (λ,1)GH=0 for all pointwise isotropy groups GH (H ∈ A), then we prove the “local-global” result that λ does not appear in the representation of G on the Orlik-Solomon algebra of A. The result is applied to complex reflection groups and to finite orthogonal groups. It may also be viewed as a combinatorial result concerning the homology of the lattice of intersections of A. A more general version of the main result is also discussed.Keywords
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