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Arrangements of hyperplanes and Lie algebra homology. (English) Zbl 0754.17024
The authors investigate the cohomology of one-dimensional local systems over complements of hyperplanes in complex affine subspaces. The main results of the paper consist of the study of “discriminantal” arrangements. The cohomology of certain local systems over them is closely connected with homology of nilpotent subalgebras of Kac-Moody type Lie bialgebras. Under certain conditions, the complete set of solutions of the Knizhnik-Zamolodchikov differential equations in terms of generalized hypergeometric integrals are given.

MSC:
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
17B55 Homological methods in Lie (super)algebras
33C80 Connections of hypergeometric functions with groups and algebras, and related topics
52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry)
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