Representation Theory
(Math 253
and Physics 293)
Fall 2008
Instructor:
Paul Aspinwall
Credits: 3.0
Time: Tu Th 1:15-2:30 PM
Location: Physics 227
Requirements
Homework
- is listed here. It may be useful to
use Maple for some of the problems.
Prerequisites
- A thorough knowledge of linear algebra.
Exams There will be a take-home final which will be due back
at 5:00pm on Wednesday, Dec 10. There may also be a midterm exam.
Synopsis
A rough outline is as follows.
- Finite Groups
- Basic definitions
- Schur's Lemma
- Characters
- Induced representations
- Real representations
- The symmetric groups and Young Diagrams
- Lie Groups and Lie Algebras
- Basic definitions
- Basic notions of classification
- Simple and semisimple Lie algebras
- Trivial low dimensional examples
- sl(2) in gory detail
- sl(3) in gory detail
- Classical Lie Algebras
- General constructions and the Killing form
- sl(n) and Young diagrams again
- sp(n)
- so(n) and spinors
- The General Classification
- Dynkin diagrams
- The exceptional algebras g2, f4, e6, e7, e8
- Characters
- Lie groups
Textbooks
The course will be based on the text:
- W. Fulton and J. Harris, Representation Theory: A First
Course, Springer-Verlag 1991.
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