Table of Contents

Introduction.; 1. Preliminaries; 2. Structure Theory of Semisimple Rings; 3. Representation Theory of Finite Groups; 4. Representation Theory of the Symmetric Group; 5. Symmetric Polynomials; 6. Schur-Weyl Duality and the Relationship Between Representations of Sd and GLn (C); 7. Structure Theory of Complex Semisimple Lie Algebras; 8. Representation Theory of Complex Semisimple Lie Algebras; 9. Generalities on Algebraic Groups; 10. Structure Theory of Reductive Groups; 11. Representation Theory of Semisimple Algebraic Groups; 12. Geometry of the Grassmannian, Flag and their Schubert Varieties via Standard Monomial Theory; 13. Singular Locus of a Schubert Variety in the Flag Variety SLn/B; 14. Applications.; Appendix: Chevalley Groups.; Bibliography.; List of Symbols.; Index.