Undergraduate Thesis Presentation: "Real Representations of Finite Groups and the Mackey Machine"

Abstract: Given an extension of finite groups 1->G->H->Q->1, the Mackey machine provides a way to construct the irreducible complex representations of H from the irreducible representations of G and the irreducible projective representations of Q. In my talk, I will introduce the basics of representation theory and discuss the differences between representations over complex vector spaces and those over real vector spaces. I will describe the Mackey machine for complex representations as well as its generalization to real representations, the main topic of my research. To illustrate the theory, I will compute the irreducible representations of the dihedral group.

Host: Xiang Tang