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# The Elliptic Hall Algebra and the K-theory of the Hilbert Scheme of a 2

@inproceedings{SchiffmannTheEH, title={The Elliptic Hall Algebra and the K-theory of the Hilbert Scheme of a 2}, author={Olivier Schiffmann and E Vasserot} }

In this paper we compute the convolution algebra in the equivariant K-theory of the Hilbert scheme of A 2. We show that it is isomorphic to the elliptic Hall algebra, and hence to the spherical DAHA of GL∞. We explain this coincidence via the geometric Langlands correspondence for elliptic curves, by relating it also to the convolution algebra in the equivariant K-theory of the commuting variety. We also obtain a few other related results (action of the elliptic Hall algebra on the K-theory of… CONTINUE READING

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