Topics in Representation Theory

Review
of semisimple Lie algebras and their finite dimensional representations. Complex Lie groups, Borel subgroups, and the Weyl group. The flag variety, vector bundles, coherent sheaves and cohomology, the Borel-Weil theorem. Double cosets, Bruhat cells and Schubert varieties. The BGG category O, blocks, and translation functors. The nilpotent cone, and Kostant’s theorem. The Iwahori-Hecke algebra. Introduction to D-modules.

References:
Chriss, Ginzburg – Representation theory and complex geometry.
Fulton, Harris – Representation theory.
Hotta, Takeuchi, Tanisaki — D-modules, perverse sheaves, and representation theory.
Humphreys – Representations of semisimple Lie algebras in the BGG category O.