Representations of complex tori and GL(2, C)

Abstract

Groups and their representations have been studied for a long time. One can extend the notion of a group by asking the group axioms to hold in other categories. A group in the category of smooth manifolds is a Lie group, and a group in the category of algebraic varieties is an algebraic group. In this paper, we discuss the representation theory of algebraic groups, in particular complex tori and GL(2,C).