MATH 6500 - Lie Groups

Allen Knutson, spring 2016.

I plan this to be a standard first Lie groups course, heading to the classification of complex (or compact) simple Lie groups and their finite-dimensional irreducible representations. Geometric/topological methods will be favored over algebraic ones (e.g. Lie algebras will not be at the forefront).

Possible additional topics, depending on interest:

• Verma modules and the Beilinson-Bernstein localization theorem
• Kac-Moody groups (especially affine) and their representations
• The geometric Satake correspondence
• Combinatorics of symmetric functions