Hall modules with applications to quantum groups and moduli spaces

Abstract

I will begin by introducing the Hall module of an exact category with duality. This plays the role of the Hall algebra when objects of the category carry non-degenerate forms. Applied to the category of quiver representations, this construction produces representations of twisted quantum Kac-Moody algebras. I will also explain how Hall modules can be used to study arithmetic aspects of moduli spaces of self-dual quiver representations and principal bundles over curves.