Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local systems over complements of hyperplanes and the Kac-Kazhdan
  conditions for singular vectors   In this note we strenghten a theorem by Esnault-Schechtman-Viehweg which
states that one can compute the cohomology of a complement of hyperplanes in a
complex affine space with coefficients in a local system using only logarithmic
global differential forms, provided certain "Aomoto non-resonance conditions"
for monodromies are fulfilled at some "edges" (intersections of hyperplanes).
We prove that it is enough to check these conditions on a smaller subset of
edges.
  We show that for certain known one dimensional local systems over
configuration spaces of points in a projective line defined by a root system
and a finite set of affine weights (these local systems arise in the geometric
study of Knizhnik-Zamolodchikov differential equations), the Aomoto resonance
conditions at non-diagonal edges coincide with Kac-Kazhdan conditions of
reducibility of Verma modules over affine Lie algebras.

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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: physics