Gale duality and Koszul duality

@article{Braden2008GaleDA,
  title={Gale duality and Koszul duality},
  author={Tom Braden and Anthony Licata and Nicholas Proudfoot and Ben Webster},
  journal={arXiv: Representation Theory},
  year={2008}
}

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References

SHOWING 1-10 OF 62 REFERENCES
Goresky-MacPherson duality and deformations of Koszul algebras
We show that the center of a flat graded deformation of a standard Koszul algebra behaves in many ways like the torus-equivariant cohomology ring of an algebraic variety with finite fixed-point set.
Projective modules in the category _{}: self-duality
Given a parabolic subalgebra ps of a complex, semisimple Lie algebra , there is a naturally defined category °s of g-modules which includes all the g-modules induced from finite-dimensional
Localization algebras and deformations of Koszul algebras
We show that the center of a flat graded deformation of a standard Koszul algebra A behaves in many ways like the torus-equivariant cohomology ring of an algebraic variety with finite fixed point
Projective-injective modules, Serre functors and symmetric algebras
Abstract We describe Serre functors for (generalisations of) the category associated with a semisimple complex Lie algebra. In our approach, projective-injective modules, that is modules which are
Electric-Magnetic Duality And The Geometric Langlands Program
The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are
A survey of hypertoric geometry and topology
Hypertoric varieties are quaternionic analogues of toric varieties, important for their interaction with the combinatorics of matroids as well as for their prominent place in the rapidly expanding
Symmetric functions, parabolic category O and the Springer fiber
We prove that the center of a regular block of parabolic category O for the general linear Lie algebra is isomorphic to the cohomology algebra of a corresponding Springer fiber. This was conjectured
Koszul Duality Patterns in Representation Theory
The aim of this paper is to work out a concrete example as well as to provide the general pattern of applications of Koszul duality to repre- sentation theory. The paper consists of three parts
POSITIVITY IN EQUIVARIANT QUANTUM SCHUBERT CALCULUS
A conjecture of D. Peterson, proved by W. Graham [Gr], states that the structure constants of the (T−)equivariant cohomology of a homogeneous space G/P satisfy a certain positivity property. In this
...
...