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A vanishing theorem for hyperplane cohomology

Published online by Cambridge University Press:  17 April 2009

G.I. Lehrer
G.I. Lehrer
Affiliation:
School of Mathematics and StatisticsUniversity of SydneySydney NSW 2006Australia
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 3 , June 1996 , pp. 361 - 368
Copyright
Copyright © Australian Mathematical Society 1996

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