Constructions of highest weight modules of double Ringel-Hall algebras via functions

In [19], Zheng studied the bounded derived categories of constructible $bar{mathbb{Q}}_l$-sheaves on some algebraic stacks consisting of the representations of a enlarged quiver and categorified the integrable highest weight modules of the corresponding quantum group by using these categories. In this paper, we shall generalize Zhengs work to highest weight modules of a subalgebra of the double Ringel-Hall algebra associated to a quiver in a functional version.