Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-11-11
J. Pure Appl. Algebra 100 (1995) 93
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, latex. A small error and a title in the bibliography are corrected
Scientific paper
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.
Schechtman Vadim
Terao Hiroaki
Varchenko Alexander
No associations
LandOfFree
Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-19152