Canonical bases of loop algebras via quot schemes II

Abstract

This paper is a sequel (and contains a better treatment) of math.QA/0404032; We construct some canonical bases for quantum toroidal algebras of types D_4, E_6, E_7, E_8 using perverse sheaves on quot schemes parametrizing equivariant coherent sheaves on elliptic curves. We also study some compatibility properties of these bases with some natural filtrations and modules.

65 pages Latex