Gale duality and Koszul duality

Tom Braden*, Anthony Licata, Nicholas Proudfoot, Ben Webster

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2002-2049
Number of pages48
JournalAdvances in Mathematics
Issue number4
Publication statusPublished - Nov 2010
Externally publishedYes


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