2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98558We 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 pagesAlgebraic GeometryCombinatoricsQuantum Algebra17B10, 32S22, 52C35, 55N25text