Brief Papers on Representation Theory

Here are some notes I have written to remind myself how various objects, concepts, and theorems work in representation theory. Please let me know if I have made any errors or if you have suggestions for other content!

Representation Theory
Representations of the symmetric group
Proof of Harish-Chandra isomorphism for sl(2,C)
Elementary injectivity of Harish-Chandra for sl(2,C)
Elementary injectivity of Harish-Chandra for sl(2,C) (v. 2.0)
Proof that K-finite vectors are invariant under g, K
Proof that smooth vectors are dense in V
Proof of (g,K) module correspondence with an application
Representations of the symmetric and general linear group