We explain basic materials in representation theory on compact Lie groups. This course is a continuation of MTH.B503.
Understand basics on Lie groups and Lie algebras with various examples
adjoint representation, invariant measure, Schur's lemma, characters, Schur orthogonality relations
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
standard lecture course
Course schedule | Required learning | |
---|---|---|
Class 1 | adjoint representation, invariant measure | Details will be provided during each class session |
Class 2 | Schur's lemma | |
Class 3 | representation theory of SU(2) | |
Class 4 | characters, Schur's orthogonality relation | |
Class 5 | fundamental properties of characters | |
Class 6 | representation theory of SU(2) and su(2) | |
Class 7 | representation theory of SU(2) and su(2) (continued) | |
Class 8 | product representation, representation of SO(4) |
none
Warner, "Foundation of differential manifolds and Lie groups" GTM 94, Chapter 3
homework
none