Date 
Topics 
Sections 
Event 
Week 1 
104 
Lie groups and Lie algebrashow they are connected 
IT pages 1323 
Reading: Ziller pages 13, 1115 and my two lectures 
106 
Construction of a local Lie group from a Lie algebra 
Week1 Notes 
Reading: Warner, Warner pages 8389 for many examples 
Week 2 
111 
Homomorphisms and subgroups and subalgebras 
Ziller 1.2, 1.3 
Reading: Ziller pages 410, 1423. See Donaldson's notes for a slightly different approach of integrating a Lie algebra 
113 
Covering groups 
IT, 1.21.4, and Week2 Notes 
Reading: Ziller pages 3035 
Week 3 
118 
Representation of compact Lie groups 
Hsi Pages 112, and Week3 Notespart A 
Reading: Ziller pages 44 (for the existence of a biinvariant nform), 9092 
120 
Representation of SU(2) 
Hsi Pages 1319, and Week3 Notespart B 
Reading: Ziller pages 9394 
Week 4 
125 
A PeterWeyl Theorem 
Warner: pages 254257, and Week4 Notespart A 
Readings: Hum 110, Ziller: 4547 
127 
Basics of Lie algebras 
Ziller pages 3640, and Week4 Notespart B 
Readings: Hum 1118 
Week 5 
21 
Cartan's theorem/Criterions 
Ziller pages 4042, Hum pages 1922and Week5 Notespart A 
Readings: Complexification notes 
23 
Structure of Semisimple Lie algebras 
Ziller pages 4245, Hum, 5.2, 5.3 and Week5 Notespart B 

Week 6 
28 
Compact Lie algebras and Weyl's theorem 
Ziller pages 4447 and Week6 Notespart A 
Readings: Hsiang pages 7883; See also IseTakeuchi, page 61 for another analytic proof of Weyl's Theorem 
210 
Maximal torus and Weyl group 
Ziller pages 4850, IseTakeuchi, pages 5255 
Readings: Hsiang pages 3847 for slightly different arguments 
Week 7 
215 
The proof of CartanWeylHopf theorem 
IseTakeuchi, pages 5257 and Week7 Notespart A 
Reading: Computations of curvature 
217 
The action of Weyl groups 
Ziller pages 50 and 5354, Hsi pages 4647, and Week7 Notespart B 
Reading: Kronecker and Hopf Lemmas 
Week 8 
222 
Root system and propertiesI 
Ziller pages 5556, IseTakeuchi pages 8485 and 8991, and Week8 Notespart A 
Readings: Hsi pages 4853, 6366 
224 
Root systems and propertiesII 
Ziller pages 5862, IseTakeuchi pages 9296, and Week8 Notespart B 
Readings: Serre, Ch 3, RootsExamples ; Compare IseTakeuchi 8689 with Humphreys 23 
Week 9 
31 
Cartan integers/matrices and Dynkin diagram 
Ziller pages 6265, and Week9 Notes 
Readings: Serre Ch 5 
33 
Classification of root systems 
Ziller pages 6669, Ziller pages 6265, Serre Ch 5 
Readings:Humphreys Section 11.4, pages 5763, Hsi, pages 97102 
Week 10 
38 
The maximal root, the highest weight and Weyl's character formulaI 
Hsi 4.3, and Week10 Notes 
Readings: Serre, pages 6465 and IseTakeuchi, pages 93109 on the relation between the compact Lie algebra and the semisimple real Lie algebras 
310 
Weyl's character formulaII 
Hsi 4.4 
Knapp's Representation Theory of SemiSimple Groups, Ch 4.7, 4.10 