Resonant local systems on complements of discriminantal arrangements and sl_2 representations

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We calculate the skew-symmetric cohomology of the complement of a discriminantal hyperplane arrangement with coefficients in local systems arising in the context of the representation theory of the Lie algebra sl_2. For a discriminantal arrangement in C^k, the skew-symmetric cohomology is nontrivial in dimension k-1 precisely when the "master function" which defines the local system on the complement has nonisolated critical points. In symmetric coordinates, the critical set is a union of lines. Generically, the dimension of this nontrivial skew-symmetric cohomology group is equal to the number of critical lines.
LaTeX, 12 pages

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Algebraic Geometry, Combinatorics, Quantum Algebra, 17B10, 32S22, 52C35, 55N25

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http://salesiana.dossiersoluciones.com/handle/123456789/98558

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0211253
 http://arxiv.org/abs/math/0211253
 Geom. Dedicata 101 (2003), 217-234

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arXiv