Duke Mathematical Journal
- Duke Math. J.
- Volume 161, Number 9 (2012), 1711-1750.
On the Hall algebra of an elliptic curve, II
The Hall algebra of the category of coherent sheaves on an elliptic curve defined over a finite field has been explicitly described and shown to be a 2-parameter deformation of the ring of diagonal invariants (in infinitely many variables). We study a geometric version of this Hall algebra, by considering a convolution algebra of perverse sheaves on the moduli spaces of coherent sheaves on . This allows us to define a canonical basis of in terms of intersection cohomology complexes. We also give a characterization of this basis in terms of an involution, a lattice, and a certain PBW-type basis.
Duke Math. J., Volume 161, Number 9 (2012), 1711-1750.
First available in Project Euclid: 6 June 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 22E57: Geometric Langlands program: representation-theoretic aspects [See also 14D24]
Secondary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
Schiffmann, Olivier. On the Hall algebra of an elliptic curve, II. Duke Math. J. 161 (2012), no. 9, 1711--1750. doi:10.1215/00127094-1593362. https://projecteuclid.org/euclid.dmj/1338987167