Month: December 2014

Merry Christmas! In the previous post I introduced the idea of an irreducible representation and showed that except in fields of low characteristic, these representations decompose completely. In this post I'll present Schur's Lemma at talk about what Schur and Maschke tell us about homomorphisms of representations. 1. Motivation Fix a group $latex {G}&fg=000000$ now,… Continue reading Representation Theory, Part 2: Schur’s Lemma →

Good luck to everyone taking the December TST tomorrow! The goal of this post is to give the reader a taste of representation theory, a la Math 55a. In theory, this post should be accessible to anyone with a knowledge of group actions and abstract vector spaces. Fix a ground field $latex {k}&fg=000000$ (for all… Continue reading Representation Theory, Part 1: Irreducibles and Maschke’s Theorem →