2nd
How I Can Tell I Have the Right Job
I was planning not to pay attention in representation theory today: I sat down in the back row with my markers out, all ready to doodle braids or work on research. And then the presenter stated the theorem she was going to prove, and I realized I had to change my plans. The theorem was Schur’s lemma, which is a couple layers too deep in definitions for this post, but which I’ll state anyway in case I have a secret algebraist follower: If you have a CG-homomorphism between two irreducible CG-modules, it’s either an isomorphism or the 0 homomorphism. Okay everyone ignore that sentence.
The point is: I am a sucker for homomorphisms. They’re functions that preserve the structure of the things they act on, but often ignore a lot of detail. A lot of problems metaphorically reduce to finding the right homomorphism.
