  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.
