On the Hall algebra of an elliptic curve. II (Q433919)

Given an elliptic curve \(E\) defined over a finite field \(\mathbb F_p\), the Hall algebra \(U^+_E\) of the category of coherent sheaves on \(E\) has been shown to be a 2-parameter deformation of the ring of diagonal invariants \(R^+ = \mathbb C [x_1^\pm, \ldots, y_1, \ldots]^{S_\infty}\). In this paper the author studies a geometric version of this Hall algebra by considering a convolution algebra of perverse sheaves on the moduli spaces of coherent sheaves on \(E\). This makes it possible to define a canonical basis of \(U^+_E\) in terms of intersection cohomology complexes. He also gives a characterization of this basis in terms of an involution, a lattice, and a certain PBW-type basis.NEWLINENEWLINE For part I, cf. [\textit{I. Burban} and the author, Duke Math. J. 161, No. 7, 1171--1231 (2012; Zbl 1286.16029)].