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

Abstract

In [26], Zheng studied the bounded derived categories of constructible Q¯l-sheaves on certain algebraic stacks consisting of the representations of a framed quiver and categorified the integrable highest weight modules of the corresponding quantum group by using these categories. In this paper, we generalize Zheng's work and realize highest weight modules of a certain subalgebra of the double Ringel-Hall algebra of a finite quiver without edge loops via spaces of functions on representation varieties.