Representations of Gan-Ginzburg algebras

Details Representations of Gan-Ginzburg algebras Representations of Gan-Ginzburg algebras

2010-01-15

arxiv.org/abs/1001.2588v2

Mathematics

Representation Theory

34 pages. Typo corrected and notation improved in the proof of Proposition 6.8

Scientific paper

Given a quiver, a fixed dimension vector, and a positive integer n, we construct a functor from the category of D-modules on the space of representations of the quiver to the category of modules over a corresponding Gan-Ginzburg algebra of rank n. When the quiver is affine Dynkin we obtain an explicit construction of representations of the corresponding wreath-product symplectic reflection algebra of rank n. When the quiver is star-shaped, but not finite Dynkin, we use this functor to obtain a Lie theoretic construction of representations of a "spherical" subalgebra of the Gan-Ginzburg algebra isomorphic to a rational generalized double affine Hecke algebra of rank n. Our functors are a generalization of the type A and type BC functors from arXiv:math/0702670 and arXiv:0801.1530 respectively.

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