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.

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.