Finite dimensional algebras and quantum groups

Contentsix§5.3. Universal enveloping algebras of Kac–Moody Lie algebras 244§5.4. Symmetry structures of Kac–Moody Lie algebras 247§5.5. Braid group actions 252§5.6. Quantum sl 2 256Exercises and notes 263Chapter 6. Quantum enveloping algebras 271§6.1. Quantum enveloping algebras 271§6.2. The elementary structure of U 275§6.3. The Hopf algebra structure of U 278§6.4. The adjoint action and triangular decomposition 283§6.5. Annihilators of integrable U-modules 289§6.6. Integrable U v (sl 2 )-modules and their symmetries 295§6.7. Symmetries of integrable U-modules 302§6.8. Symmetry of U and braid group actions 305§6.9. An integral structure 308§6.10. A PBW theorem for finite type 315Exercises and notes 318Part 3. Representations of Symmetric GroupsChapter 7. Kazhdan–Lusztig combinatorics for Hecke algebras 325§7.1. R-polynomials and Kazhdan–Lusztig bases 326§7.2. Multiplication formulas and Kazhdan–Lusztig polynomials 328§7.3. Inverse Kazhdan–Lusztig polynomials and dual bases 332§7.4. Cells 335§7.5. Knuth and Vogan classes 338§7.6. q-permutation modules and their canonical bases 342§7.7. Cell modules and the Ext 1 -vanishing property 349§7.8. The positivity property 353Exercises and notes 361Chapter 8. Cells and representations of symmetric groups 367§8.1. The row-insertion algorithm 368§8.2. The RSK correspondence 370§8.3. The symmetry of the RSK correspondence 375§8.4. Knuth equivalence classes in S r 379