Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors

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dc.creatorSchechtman, V.
dc.creatorTerao, H.
dc.creatorVarchenko, A.
dc.date1994-11-11
dc.date1994-12-22
dc.date.accessioned2026-07-07T09:03:50Z
dc.date.available2026-07-07T09:03:50Z
dc.descriptionIn 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.
dc.description10 pages, latex. A small error and a title in the bibliography are corrected
dc.identifierhttps://arxiv.org/abs/hep-th/9411083
dc.identifierhttp://arxiv.org/abs/hep-th/9411083
dc.identifierJ. Pure Appl. Algebra 100 (1995) 93
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/149160
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subjectQuantum Algebra
dc.titleLocal systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors
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