Resonant Local Systems on Complements of Discriminantal Arrangements and Sl2Representations
Resonant Local Systems on Complements of Discriminantal Arrangements and Sl2Representations
复制标题
判别排列和 Sl2 表示补集的局部共振系统
DOI：
10.1023/a:1026370732724
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发表时间：
2002
影响因子：
0.5
通讯作者：
A. Varchenko
中科院分区：
文献类型：
--
作者：
Daniel C. Cohen;A. Varchenko
AbstractWe 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
$$\mathfrak{s}\mathfrak{l}_2$$
. 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 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.
