Resonant local systems on complements of discriminantal arrangements and s-fraktur sign l-fraktur sign2 representations

Document Type

Article

Publication Date

1-1-2003

Abstract

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 s-fraktur sign l-fraktur sign2. For a discriminantal arrangement in Ck, 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.

Publication Source (Journal or Book title)

Geometriae Dedicata

First Page

217

Last Page

234

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