Representation Theory, Math 9140b, Winter 2010

This course will study the representation theory of finite groups and Lie groups, with a focus on the symmetric groups and linear groups, and the relationships between these two. Basic background in group theory, modules and linear algebra will be assumed.


Basic representation theory: irreducibility, complete reducibility, Schur's lemma, character theory, induced representations, etc.

Representations of the symmetric groups: partitions, Young tableaux, Young symmetrizers, Specht modules, and lots more.

Representations of the special and general linear groups: polynomial and rational representations, complete reducibility, characters, tensor representations, and lots more.

Text: There is no text for the course. Some references you may like to use:

Homework: Homework will be due roughly every two weeks. I encourage discussion of the class material with other students, and I encourage you to consult textbooks to learn more. But don't copy solutions from students or texts, and when a student or a text helps you solve a problem, you should give credit.

Presentations: In the second half of the semester, each student will give a presentation on a topic related to the course.

Exam: There will be a final exam at the end of the course.

Evaluation: Evaluation will be based upon homework (40%), presentations (30%) and the final exam (30%).

Back to Dan Christensen's home page.

Western Mathematics Home Page