Journal
ADVANCES IN MATHEMATICS
Volume 225, Issue 4, Pages 2002-2049Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2010.04.011
Keywords
Hyperplane arrangements; Gale duality; Koszul duality; Category O
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Funding
- NSA [H98230-08-1-0097]
- Clay Liftoff Fellowship
- NSF [DMS-0738335]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0950383] Funding Source: National Science Foundation
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Given a hyperplane arrangement in an affine space equipped with a linear functional, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul dual to each other, and that the roles of the two algebras are reversed by Gale duality. We also study the centers and representation categories of our algebras, which are in many ways analogous to integral blocks of category O. (C) 2010 Elsevier Inc. All rights reserved.
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