# Math 210C: Graduate Algebra (Spring 2017)

## Lie Theory

This class will meet 1:15 on Tuesdays and Thursdays in 381T
The course will over basic representation theory of compact Lie Groups
through the Weyl Character theory, and one additional topic (probably
Schur-Weyl duality).

The text will be Bump *Lie Groups, Second Edition*. The book
is available on-line through the Stanford libraries.

Of the first four Chapters of the book, we will only cover
Chapter 2. Then we will begin with Chapter 5 and continue
through Chapter 22 with some omissions. After that, there
will be some time and we may talk about topics in Chapters 25
and 26.

Although this is an algebra course, there will be a bit of
analysis. (The course will become more algebraic as it goes along.)

### Special Lecture

Persi Diaconis will teach the class of Tuesday, May 23.

### Typos

I hope there will be a third edition of the book. Therefore
**Please report any typos you find!** Also, anything that is
not clear, etc.

## Office Hours

Mondays at noon, Tuesdays at 3 PM and Wednesdays at 12 noon. Other
times if I'm free and in my office.

## Homework

If you submit your solutions electronically, please use bump at
math dot stanford dot edu, and put Math210C in the message heading.

- Homework 1: Due Wednesday, April 12: Chapter 2, Problems 2.1-2.4.
- Homework 2: Due Wednesday, April 19: Chapter 5, Problems 1,2,3,6,7,8. The version posted
is slightly different from what is in the book.
**Note:** in
Exercise 5.8, the version posted until April 13 included the
case $F=\mathbb{H}$ and $G=Sp(4)$. However the exercise is
not correct in this case, so I have taken that case out.
- Homework 3: Due Wednesday, April 26: Chapter 5, Problem 9.
Chapter 7, Problems 1 and 3. Chapter 10, Problems 1 and 2.
- Homework 4: Due Wednesday, May 3: Chapter 12, Problems 1,2,3.
Chapter 15, Problem 1.
- Homework 5: Due Wednesday, May 10: Chapter 17, Problems 1,4,5
Chapter 18, Problem 1,2.
- Homework 6: Due Wednesday, May 17: Chapter 19, Problems 2,3,4
Chapter 21, Problem 1.
- Homework 7: Due Friday, May 25: Chapter 22. Do any 5 exercises.
Corrections to Problems 22.15 and 22.16.
This will be the last homework.

## Sage

Sage mathematicsal
software can do many typical Lie group computations such as
tensor products and branching rules, listing the
maximal subgroups, computations in the Weyl group,
action of the Weyl group on roots, Frobenius-Schur
inicators, Hecke algebras and crystal bases, and
more.