For this course some knowledge of basic material on Lie groups and Lie algebras is assumed, although this will be reviewed briefly at the start of the course.
Plan:
Simple complex Lie algebras and compact Lie groups. Symmetric spaces. The geometry of co-adjoint orbits and representations of compact Lie groups (Borel-Weil Theorem). Some structure theory (Weyl group, root systems etc.). Spin representations and some exceptional Lie groups. Representations of SL(2,R) and the Selberg Trace formula.