Representation theory of compact Lie groups Lie groups, Lie algebras, matrix groups , representations, Schur’s orthogonality relations, Peter-Weyl theorem, structure of compact semisimple Lie groups, maximal tori, roots and rootspaces, classification of fundamental systems Weyl group, Highest weight theorem, Weyl integration formula, Weyl’s character formula. References
- Knapp, A.W., Representation Theory of Semisimple Lie Groups: An Overview Based on Examples, Princeton University Press, 2002.
- Hall, B.C., Lie Groups, Lie Algebras and Representations, Springer-Verlag, 2003.
- Simon, B., Representations of Finite and Compact Groups, AMS, 1996.
- Varadarajan, V.S., Lie Groups, Lie Algebras and their Representations, Sringer-Verlag, 1984.