# On the Hall algebra of an elliptic curve, I

@article{Burban2005OnTH, title={On the Hall algebra of an elliptic curve, I}, author={I. I. Burban and Olivier Schiffmann}, journal={Duke Mathematical Journal}, year={2005}, volume={161}, pages={1171-1231} }

This paper is a sequel to math.AG/0505148, where the Hall algebra U^+_E of the category of coherent sheaves on an elliptic curve E defined over a finite field was explicitly described, and shown to be a two-parameter deformation of the ring of diagonal invariants R^+=C[x_1^{\pm 1}, ..., y_1,...]^{S_{\infty}} (in infinitely many variables). In the present work, we study a geometric version of this Hall algebra, by considering a convolution algebra of perverse sheaves on the moduli spaces of…

## 151 Citations

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We compare the (horizontal) trace of the affine Hecke category with the elliptic Hall algebra, thus obtaining an “affine” version of the construction of [14]. Explicitly, we show that the…

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