The topics include:
- Unitary representation of finite groups
- complete reducibility
- character theory
- Lie groups and Lie algebras
- basic correspondence between Lie groups and Lie algebras
- solvable vs. semisimpe Lie algebras
- Simple Lie groups
- compact vs. complex Lie algebras
- maximal torus and Cartan subalgebras
- root system and Weyl group
- Dynkin diagrams
- highest weight theory
- Advanced topics: (some of)
- general compact groups, Haar measure, Peter-Weyl theorem...
- representation of symmetric groups, Schur-Weyl duality...
- flag manifolds, Borel-Weil-Bott theorem...
- induced representations, Mackey's criterion, Artin's theorem...
Primary text
- Fulton, William; Harris, Joe. Representation theory. A first course. Graduate Texts in Mathematics, 129. Readings in Mathematics. Springer-Verlag, New York, 1991. xvi+551 pp. ISBN: 0-387-97527-6; 0-387-97495-4
Further readings
- Serre, Jean-Pierre. Linear representations of finite groups. Graduate Texts in Mathematics, Vol. 42. Springer-Verlag, New York-Heidelberg, 1977. x+170 pp. ISBN: 0-387-90190-6
- Bourbaki, Nicolas. Lie groups and Lie algebras. Chapters 1–3. Elements of Mathematics. Springer-Verlag, Berlin, 1998. xviii+450 pp. ISBN: 3-540-64242-0
- Bourbaki, Nicolas. Lie groups and Lie algebras. Chapters 4–6. Elements of Mathematics. Springer-Verlag, Berlin, 2002. xii+300 pp. ISBN: 3-540-42650-7
- Bourbaki, Nicolas. Lie groups and Lie algebras. Chapters 7–9. Elements of Mathematics. Springer-Verlag, Berlin, 2005. xii+434 pp. ISBN: 3-540-43405-4