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- W1630607406 abstract "We introduce deformed preprojective attached to infinite affine Dynkin quivers of type A_{infty}, A_{+infty}, D_{infty}. We define a one-parameter family of deformations of the wreath product of a symmetric group with these algebras and, using the generalized McKay correspondence for infinite reductive subgroups of SL(2,C), we establish a Morita equivalence to a corresponding continuous symplectic reflection algebra of wreath product type. We give applications of this Morita equivalence to the representation theory of continuous wreath product symplectic reflection algebras. In particular, we use Crawley-Boevey and Holland's results about the representation theory of deformed preprojective algebras to get a complete classification of the finite dimensional irreducible representations for the rank one continuous wreath product symplectic reflection algebras. In higher rank, we extend Gan's definition of the reflection functors to the continuous case and we use such functors to find an interesting class of finite dimensional representations." @default.
- W1630607406 created "2016-06-24" @default.
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- W1630607406 date "2006-12-04" @default.
- W1630607406 modified "2023-09-27" @default.
- W1630607406 title "Reflection functors and representations for continuous wreath-product symplectic reflection algebras" @default.
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