A Lie group is a group G which at the same time
is a smooth manifold such that the group law G x G
-> G is a smooth map. Lie groups occur
naturally as transformation groups of geometric
objects. Typical examples are matrix groups like
SL(n,R) or SO(n). In the lecture we introduce the
general theory of Lie groups with a special focus
on compact groups and their representation theory
culminating in the complete description of
representations through Highest Weight Theory.
Vorausgesetzte Kenntnisse / Necessary previous
Bump, D.: Lie Groups. Springer-Verlag.
Warner, F.: Foundations of Differentiable Manifolds and Lie Groups. Springer-Verlag.
/Examination requirements: Active
participation in the problem class.