Gale duality and Koszul duality
By Tom Braden, Anthony M. Licata, Nicholas Proudfoot, Ben Webster. 2008
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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.
View Paper: https://www.semanticscholar.org/paper/0f354491897220f5d578a1717f01494f6f4d5719
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Citations in the corpus
- 2-block Springer fibers: convolution algebras and coherent sheaves (2008, background): “ries (see Section 5 for results in this direction). An analogous construction associating an algebra to a hypertoric variety has been developed by the second author with Braden, Licata and Proudfoot ([BLPW08]). Like the algebra we define, this hypertoric algebra is quasi-hereditary and moreover Koszu”