T. Braden

Abstract:   Given a simple hyperplane arrangement and a generic covector we define an associative algebra whose representations we call the "category O" of the arrangement. It is analogous to the category O from the representation theory of Lie algebras, with the role of the cotangent bundle of the flag variety played by a hypertoric variety (a hyperkaehler quotient of the cotangent bundle to affine space by an action of a torus). A number of results from representation theory have analogues for this new algebra; in particular it is quasi-hereditary and Koszul. The Koszul dual algebra is given by the same construction for the Gale dual arrangement, and also by a Ginzburg-type convolution algebra on certain Lagrangian toric varieties inside the hypertoric variety.

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