Resonant Local Systems on Complements of Discriminantal Arrangements and Sl2Representations |
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Authors: | Daniel C Cohen Alexander N Varchenko |
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Institution: | (1) Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, U.S.A.;(2) Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, U.S.A. |
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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
. For a discriminantal arrangement in 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 criticalpoints. 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. |
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Keywords: | discriminantal arrangement
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