Resonant local systems on complements of discriminantal arrangements and sl_2 representations

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dc.creatorCohen, Daniel C.
dc.creatorVarchenko, Alexander N.
dc.date2002-11-16
dc.date.accessioned2026-07-07T06:31:17Z
dc.date.available2026-07-07T06:31:17Z
dc.descriptionWe 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.
dc.descriptionLaTeX, 12 pages
dc.identifierhttps://arxiv.org/abs/math/0211253
dc.identifierhttp://arxiv.org/abs/math/0211253
dc.identifierGeom. Dedicata 101 (2003), 217-234
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98558
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subjectQuantum Algebra
dc.subject17B10, 32S22, 52C35, 55N25
dc.titleResonant local systems on complements of discriminantal arrangements and sl_2 representations
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