Math 423 Spring 2006: Lie groups
Lecture time: MTW 1-2, Gilman
110. Office hours (walk-in): M 2-5 Krieger 312.
Textbook: Howard Georgi, Lie
algebras in particle physics, second edition, Westview Press.
Lecture notes
Lecture 1:
Basic concepts in group theory.
Lecture 2:
Group representations.
Lecture 3:
Weyl trick and Schur lemma.
Lecture 4:
Orthogonality Relations.
Lecture 5:
Character table. Tensor products.
Lecture 6:
The exponential map on matrix groups.
Lecture 7:
Lie groups and Lie algebras.
Lecture 8:
Compact Lie groups.
Lecture 9:
Peter-Weyl Theorem.
Lecture 10:
The dual of SU(2) and special functions on S3.
Lecture 11:
Spherical harmonics.
Lecture 12:
The dual of SU(3).
Lecture 13:
Weyl character formula.
Homework
Finite groups: Hw1 Hw2 Hw3
Hw4
Lie groups: Hw5 Hw6 Hw7 Hw8 Hw9 Hw10