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

- V. S. Varadarajan: Lie groups, Lie algebras and their representations, Sringer 1984
- B. C. Hall: Lie groups, Lie algebras and representations, Springer 2003
- Barry Simon: Representations of finite and compact groups, AMS 1996
- A. W. Knapp: Representation theory of semismiple lie groups. An overview based on examples, Princeton university press 2002.

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

- V. S. Varadarajan: Lie groups, Lie algebras and their representations, Sringer 1984
- B. C. Hall: Lie groups, Lie algebras and representations, Springer 2003
- Barry Simon: Representations of finite and compact groups, AMS 1996
- A. W. Knapp: Representation theory of semismiple lie groups. An overview based on examples, Princeton university press 2002.

Last updated: 17 May 2024