Symmetric Functions and Hall Polynomials

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Preface to the second edition......Page 6
Preface to the first edition......Page 8
Contents......Page 10
1. Partitions ......Page 12
2. The ring of symmetric functions ......Page 28
3. Schur functions ......Page 51
4. Orthogonality ......Page 73
5. Skew Schur functions ......Page 80
6. Transition matrices ......Page 110
7. The characters of the symmetric groups ......Page 123
8. Plethysm ......Page 146
9. The Littlewood-Richardson rule ......Page 153
Appendix A: Polynomial functors and polynomial representations ......Page 160
Appendix B: Characters of wreath products ......Page 180
1. Finite o-modules ......Page 190
2. The Hall algebra ......Page 193
3. The LR-sequence of a submodule ......Page 195
4. The Hall polynomial ......Page 198
Appendix (by A. Zelevinsky): Another proof of Hall's theorem......Page 210
1. The symmetric polynomials R). ......Page 215
2. Hall-Littlewood functions ......Page 219
3. The Hall algebra again ......Page 226
4. Orthogonality ......Page 233
5. Skew Hall-Littlewood functions ......Page 237
6. Transition matrices ......Page 249
7. Green's polynomials ......Page 257
8. Schur's Q-functions ......Page 261
1. The groups Land M ......Page 280
2. Conjugacy classes ......Page 281
3. Induction from parabolic subgroups ......Page 284
4. The characteristic map ......Page 287
5. Construction of the characters ......Page 291
6. The irreducible characters ......Page 295
Appendix: proof of (5.1) ......Page 302
1. Local fields ......Page 303
2. The Hecke ring H(G, K) ......Page 304
3. Spherical functions ......Page 309
4. Hecke series and zeta functions for GLn(F) ......Page 311
5. Hecke series and zeta functions for GSP2n(F) ......Page 313
1. Introduction ......Page 316
2. Orthogonality ......Page 320
3. The operators D......Page 326
 4. The symmetric functions PA(x; q, t) ......Page 332
5. Duality ......Page 338
6. Pieri formulas ......Page 342
7. The skew functions PAl,.,,' QA/,. ......Page 354
8. Integral forms ......Page 363
9. Another scalar product ......Page 379
10. Jack's symmetric functions ......Page 387
1. Gelfand pairs and zonal spherical functions ......Page 399
2. The Gelfand pair (S2n, Hn) ......Page 412
3. The Gelfand pair (GL,,(R), D(n? ......Page 425
4. Integral formulas ......Page 435
5. The complex case ......Page 451
6. The quaternionic case ......Page 457
BIBLIOGRAPHY ......Page 468
NOTATION ......Page 478
INDEX ......Page 484