Study topics

(added Feb 20) Vogan diagrams and classification of simple real Lie algebras.

Universal covering groups and computing fundamental groups

Proof of Peter-Weyl theorem and examples of representations of compact Lie groups.

Realizations of representations of compact Lie groups

Homogeneous manifolds

Representations of nilpotent Lie groups.

Infinite-dimensional representations of semisimple Lie groups

The Heisenberg group and the metaplectic representation.

Levi decompositions of Lie algebras and Lie groups

Integration and Haar measure on Lie groups