  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.
