Proudfoot, NicholasHilburn, Justin2016-10-272016-10-272016-10-27https://hdl.handle.net/1794/20456In this thesis I show that indecomposable projective and tilting modules in hypertoric category O are obtained by applying a variant of the geometric Jacquet functor of Emerton, Nadler, and Vilonen to certain Gel'fand-Kapranov-Zelevinsky hypergeometric systems. This proves the abelian case of a conjecture of Bullimore, Gaiotto, Dimofte, and Hilburn on the behavior of generic Dirichlet boundary conditions in 3d N=4 SUSY gauge theories.en-USAll Rights Reserved.3d N=4Boundary conditionCategory OHypertoricSymplectic dualitySymplectic resolutionElectronic Thesis or Dissertation