Gale duality and Koszul duality
Representation Theory
2022-11-18 v2 Algebraic Geometry
Combinatorics
Abstract
Given an affine hyperplane arrangement with some additional structure, 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.
Cite
@article{arxiv.0806.3256,
title = {Gale duality and Koszul duality},
author = {Tom Braden and Anthony Licata and Nicholas Proudfoot and Ben Webster},
journal= {arXiv preprint arXiv:0806.3256},
year = {2022}
}
Comments
55 pages; v2 contains significant revisions to proofs and to some of the results. Section 7 has been deleted; that material will be incorporated into a later paper by the same authors