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Abstract:
The orbifold cohomology of symplectic orbifolds
can be interpreted as Hochschild cohomology
of their quantizations. This fact implies that the n-th symmetric power
of a quantization of a symplectic 2-surface (n > 1) has a nontrivial
deformation, not coming from a deformation of the surface itself.
This deformation should be viewed as a (deformation of the) Hilbert
scheme Hilbn of the quantized surface. In the simplest case when the
classical surface is the 2-plane, this deformation is the (rational)
Cherednik algebra.
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