1
Lie Groups
Definition and properties of Lie groups
2
Torus Actions
Actions of a torus and weight space decomposition
3
Root Systems
Root systems obtained from the weight decomposition of the adjoint representation
4
Borel Subgroups
Dynkin diagrams, ADE classification, and flag varieties
5
Bruhat Decomposition
Cell decomposition of homogeneous spaces, parabolic subgroups, and Schubert varieties on Grassmannians
6
Richardson Varieties and Peterson Varieties
Richardson varieties as transversal intersections of opposite Schubert varieties, and Peterson varieties fr...