NMAK18005U Introduction to Representation Theory

The main emphasis will be on finite dimensional complex representations of linear groups, but infinite dimensional representations of specific groups will also be discussed. 

We begin with fundamental results such as Schur's Lemma and Mascheke's Theorem. Fundamental constructions such as tensor product representations  and dual (contragredient) are then discussed. 

The first major topic is compact groups culminating with a proof of the Peter - Weyl Theorem. The Haar measure will be mentioned and the Lie algebra of a linear group will be discussed. Time permitting we will then discuss finite-dimensional as well as infinite dimensional representations of specific Lie groups.