# 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.