On the Hall algebra of an elliptic curve, II

Details On the Hall algebra of an elliptic curve, II On the Hall algebra of an elliptic curve, II

2005-08-28

arxiv.org/abs/math/0508553v2

Mathematics

Representation Theory

25 pages, Latex, several changes made in the presentation

Scientific paper

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 coherent sheaves on E. This allows us to define a "canonical basis" B of U^+_E 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. Finally we provide some (loose) interpretation of the above construction in terms of Schubert varieties in (nonexistent!) "double affine grassmanian", and in terms of character sheaves of loop groups (both of type A).

Affiliated with

Also associated with

No associations

Rating

On the Hall algebra of an elliptic curve, II does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Hall algebra of an elliptic curve, II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Hall algebra of an elliptic curve, II will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-405184