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

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