Representation Theory by an Unhappy Guy

Why Unhappy? --- Potential to have no PhD to read.

Here are some mathematics I like very much. 

> Lecture 1 Temperley–Lieb Category [Note [Record(Chinese)] 

(Typo: Catalan number should be $\frac{1}{N+1}\binom{2N}{N}$)

> Lecture 2 Classic Invariant Theory [Notes] [Recording(Chinese)]

(Note: the corresponding adjoint invariant of e in D-type is Pffafian)

> Lecture 3 Crystal Basis Combinatorics [Notes] [Not recorded]

Typo: 

 

> Lecture 4 Quiver Representations [Quiver1]

> Lecture 5 Quiver Representations [Quiver2]

> Lecture 6 Quiver Representations (Hall algebras) (Later)

> Lecture 7 KLR Algebras [KLR1(revised).pdf]

> Lecture 8 KLR Algebras [KLR2(revised).pdf]

> Lecture 9 KLR Algebras [KLR3.pdf]

> Lecture 10 Borel Weil Theory [BorelWeil.pdf]

Contents
1 Lecture 1 — Borel–Weil Theorem
2 Lecture 2 — Demazure Character Formula
3 Lecture 3 — Schur–Weyl Modules
4 Lecture 4 — Horn’s Problem