Group theory II
The main purpose of this course is to provide for graduated students whose major are "theoretical condensed matter physics" or "theoretical physics" the essential knowledge of group theory and useful techniques applicable for solving physics problems.
Tentative contents (Group Theory II is the continued contents of Group Theory I)
I. Basic Concepts
1. Introductory Concepts
II. Discrete Groups
2. Finite Group Related to Symmetries in Physics
3. Application Examples
4. Permutation Group, Braid Group and Knot theory
III. Continuous Groups
5. The Classical Group: Group of Transformation
6. Lie Groups
7. Lie Groups and Lie Algebras
8. Topological Properties of Lie Groups
9. Root Space and Dynkin Diagrams
10. Weight Space and Representations
IV* Advanced Topics
11. Affine Lie Algebras
12. Quantum Groups and Noncommutative Geometry
R. Gilmore, Lie Group, Lie Algebra and Some of Their Applications, (Dover Publications) .
R.N. Cahn, Simple Lie Algebras and their Representations.
G. Racah, Group theory and spectroscopy.