Dates of lectures 
Description 
Notes 
Comments 
9/7

Basic concepts 
Sec 1 
(unchanged) 
9/12

Ideals 
Sec 2 

9/14

Nilpotent and solvable algebras 
Sec 3 
Promised revision not ready. 
9/19

Jordan decomposition and Cartan's criterion 
Sec 4 
correct proof that y in M added. 
9/21

Semisimple algebras and the Killing form 
Sec 5 

9/26

Casimir operator and Weyl's Theorem 
Sec 6 

9/28

Representations of sl(2,F) 
Sec 7 footnote 
plus a part of sec 6 
10/3

Root space decomposition 
Sec 8 

10/5

Root strings 
Sec 8b 
some misprints corrected 
10/10

Abstract root systems 
Sec 9 
misprints corrected. 

Examples in R^{3} 
A3, B3, C3 
animation by Sonja Igusa. 

Updated animation 
newB3, newC3 
simple roots in green, negative root behind wall 
10/12

Weyl chambers 
Sec 10 
corrected 
10/19

Classification part a 
Sec 11 
Dn, Cn 
10/24

Exceptional algebras 
Sec 12 

10/26

Isomorphism Theorem 
Sec 14 

10/31

Cartan subalgebras 
Sec 15 

11/02

Conjugacy of CSA's 
Sec 16a 
using topology! 
11/07

Conjugacy of Borel subalgebras 
Sec 16b 

11/09

Universal enveloping algebra 
Sec 17a 


Proof of PBW 
Sec 17b 
We will skip this. 
11/14

Weights and maximal vectors 
Sec 20 
final version 
11/16

Finite dimensional modules 
Sec 21 
final version 
11/21

Formal characters 
Sec 22a 
half of this section 
11/28

Weyl character formula and Schur polynomials 
Sec 22b 

11/30

Schur functors 
Sec 23, Worksheet 
notes extended 
12/05

First character formula 
Sec 24a 
beginning of the proof 
12/07

Weyl character formula 
Sec 24b 
end of the proof 

Combined notes 
Sec 124 
complete! 