Math 549: Lie Groups
Spring 2020
Instructor: Kristen Hendricks
Office: Hill Center 515
Office Hours: MW 4-5. Please let me know by email if you are coming. Also, feel free to make appointments for other times.
Email: kristen. hendricks at rutgers.edu
Location and Time
MW 1:40-3:00 in Hill 423.Prerequisites
Real Analysis, Linear Algebra, and Elementary Topology or permission of the instructor.
Topics
This is a first course in Lie groups. We will discuss roughly the following.
This is probably a little too much in total; the last few topics on the list will be selected among based on student interest.
References
Primary references:
Other Books:
Other online resources:
Representation theory overview:
Differential geometry:
Algebraic topology:
Vector bundles:
Assignments
Homework will be posted here approximately weekly. (Because we start on a Wednesday, the first assignment corresponds to the first three lectures.) You should plan to hand in roughly half the homework exercises to be checked for completion. If I see no homework at all from you, you are at risk of getting an A-.
Exercises for Lectures 1, 2, and 3
Exercises for Lectures 4 and 5
Exercises for Lectures 6 and 7
Exercises for Lectures 8 and 9
Exercises for Lectures 10 and 11
Exercises for Lectures 12 and 13
Exercises for Lectures 14 and 15
Exercises for Lectures 16 and 17
Exercises for Lectures 18 and 19
Exercises for Lectures 20 and 21
Exercises for Lectures 22 and 23
Exercises for Lectures 24 and 25
Exercises for Lectures 26, 27, and 28
Notes
Here are the scanned lecture notes from our course. These notes are intended for students in the course to follow along with the lecture.Lecture 1 Ref: Teleman Sections 1-15, Gruson and Serganova Chapters 1 and 2
Lecture 2 Ref: Teleman Sections 1-15, Gruson and Serganova Chapters 1 and 2
Lecture 3 Ref: Teleman Sections 1-15, Gruson and Serganova Chapters 1 and 2
Lecture 4 Ref: Lee Chapters 1 and 2
Lecture 5 Ref: Lee Chapter 5, Kirillov Chapter 2, Bump Chapter 5 and 7
Lecture 6 Ref: Bump Chapter 13, Hatcher Chapter 1.
Lecture 7 Ref: Lee Chapter 7, Kirillov Chapter 2 Sections 4 and 5
Lecture 8 Ref: Lee Chapter 7, Bump Chapters 6 and 7, Kirillov Chapter 3
Lecture 9 Ref: Lee Chapter 3 and 15, Bump Chapters 6 and 7, Kirillov 3.3-5
Lecture 10 Ref: Bump Chapter 8, Kirillov 3.1-2, Lee Chapter 15
Lecture 11 Ref: Bump Chapter 14 and 15, Kirillov 3.8-9, Lee Chapter 15
Lecture 12 Ref: Kirillov 4.1-4, Bump Chapter 1
Lecture 13 Ref: Kirillov 3.4-6, 4.5-6, Bump Chapter 1-2
Lecture 14 Ref: Bump Chapter 2, Kirillov 4.7
Lecture 15 Ref: Bump Chapter 2-4, 15, Kirillov 4.7
Lecture 16 Ref: Bump Chapter 3, Kirillov 4.7
Lecture 17 Ref: Bump Chapter 4, Kirillov 4.7
Lecture 18 Ref: Bump Chapter 12, Kirillov 4.8
Lecture 19 Ref: Kirillov 4.9
Lecture 20 Ref: Mitchell's notes here
Lecture 21 Ref: As previous lecture
Lecture 22 Ref: Bump Chapter 16, see also Spivak Chapter 9
Lecture 23 Ref: As previous lecture
Lecture 24 Ref: Bump Chapter 17
Lecture 25 Ref: Bump Chapter 18, see also Chapter 7 of Kirillov
Lecture 26 Ref: Bump Chapter 18, see also Chapter 7 of Kirillov