MATH 6500: Lie Groups (Spring 2010)

Instructor: Allen Knutson

What we'll definitely cover:

  1. Definition of, and going back and forth between, Lie groups and Lie algebras.
  2. Definition of a representation, and the adjoint representation.
  3. Weights and roots.
  4. Complexifying the Lie algebra. Representations of sl(2).
  5. Dynkin diagrams and the classification of complex simple Lie algebras.
  6. The classification of compact Lie groups.
  7. Representation theory of compact Lie groups.
  8. The universal enveloping algebra.

What we might have time to touch on:

  1. The Iwasawa decomposition of a general connected Lie group.
  2. The Weyl character formula and Kostant multiplicity formula.
  3. Coadjoint orbits and their cell decomposition.
  4. Algebraic groups.