Symmetric functions and Hall polynomials:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1995
|
| Edition: | 2. ed. |
| Series: | Oxford mathematical monographs
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 475 S. graph. Darst. |
| ISBN: | 0198534892 |
Staff View
MARC
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| 100 | 1 | |a Macdonald, Ian G. |d 1928- |e Verfasser |0 (DE-588)123369258 |4 aut | |
| 245 | 1 | 0 | |a Symmetric functions and Hall polynomials |c I. G. Macdonald |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Oxford |b Clarendon Press |c 1995 | |
| 300 | |a X, 475 S. |b graph. Darst. | ||
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| 650 | 4 | |a Abelian groups | |
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| 650 | 4 | |a Hall polynomials | |
| 650 | 4 | |a Symmetric functions | |
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Record in the Search Index
| _version_ | 1804124526367211520 |
|---|---|
| adam_text | Contents
I. SYMMETRIC FUNCTIONS
1. Partitions 1
2. The ring of symmetric functions 17
3. Schur functions 40
4. Orthogonality 62
5. Skew Schur functions 69
6. Transition matrices 99
7. The characters of the symmetric groups 112
8. Plethysm 135
9. The Littlewood Richardson rule 142
Appendix A: Polynomial functors and polynomial representations 149
Appendix B: Characters of wreath products 169
II. HALL POLYNOMIALS
1. Finite o modules 179
2. The Hall algebra 182
3. The L/? sequence of a submodule 184
4. The Hall polynomial 187
Appendix (by A. Zelevinsky): Another proof of Hall s theorem 199
III. HALL LITTLEWOOD SYMMETRIC
FUNCTIONS
1. The symmetric polynomials Rk 204
2. Hall Littlewod functions 208
3. The Hall algebra again 215
4. Orthogonality 222
5. Skew Hall Littlewood functions 226
6. Transition matrices 238
7. Green s polynomials 246
8. Schur s Q functions 250
IV. THE CHARACTERS OF GLn OVER
A FINITE FIELD
1. The groups L and M 269
2. Conjugacy classes 270
3. Induction from parabolic subgroups 273
4. The characteristic map 276
5. Construction of the characters 280
X CONTENTS
6. The irreducible characters 284
Appendix: proof of (5.1) 291
V. THE HECKE RING OF GLn OVER
A LOCAL FIELD
1. Local fields 292
2. The Hecke ring H(G, K) 293
3. Spherical functions 298
4. Hecke series and zeta functions for GLn(F) 300
5. Hecke series and zeta functions for GSp2n(F) 302
VI. SYMMETRIC FUNCTIONS WITH
TWO PARAMETERS
1. Introduction 305
2. Orthogonality 309
3. The operators D n 315
4. The symmetric functions Px(x; q, t) 321
5. Duality 327
6. Pieri formulas 331
7. The skew functions PA/M, QK/fL 343
8. Integral forms 352
9. Another scalar product 368
10. Jack s symmetric functions 376
VII. ZONAL POLYNOMIALS
1. Gelfand pairs and zonal spherical functions 388
2. The Gelfand pair (S2n, Hn) 401
3. The Gelfand pair (GLn(R), OM) 414
4. Integral formulas 424
5. The complex case 440
6. The quaternionic case 446
BIBLIOGRAPHY 457
NOTATION 467
INDEX 473
|
| any_adam_object | 1 |
| author | Macdonald, Ian G. 1928- |
| author_GND | (DE-588)123369258 |
| author_facet | Macdonald, Ian G. 1928- |
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| author_sort | Macdonald, Ian G. 1928- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 SK 230 SK 260 |
| classification_tum | MAT 105f |
| ctrlnum | (OCoLC)30733523 (DE-599)BVBBV010131653 |
| dewey-full | 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:47:04Z |
| institution | BVB |
| isbn | 0198534892 |
| language | English |
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| physical | X, 475 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | Oxford mathematical monographs |
| spelling | Macdonald, Ian G. 1928- Verfasser (DE-588)123369258 aut Symmetric functions and Hall polynomials I. G. Macdonald 2. ed. Oxford Clarendon Press 1995 X, 475 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Algebraïsche groepen gtt Fonctions symétriques ram Groupes abéliens ram Groupes finis ram Symmetrische groepen gtt Abelian groups Finite groups Hall polynomials Symmetric functions Abelsche Gruppe (DE-588)4140988-7 gnd rswk-swf Hall-Polynom (DE-588)4158856-3 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Symmetrische Funktion (DE-588)4342453-3 gnd rswk-swf Hall-Polynom (DE-588)4158856-3 s Symmetrische Funktion (DE-588)4342453-3 s DE-604 Abelsche Gruppe (DE-588)4140988-7 s Endliche Gruppe (DE-588)4014651-0 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006728988&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Macdonald, Ian G. 1928- Symmetric functions and Hall polynomials Algebraïsche groepen gtt Fonctions symétriques ram Groupes abéliens ram Groupes finis ram Symmetrische groepen gtt Abelian groups Finite groups Hall polynomials Symmetric functions Abelsche Gruppe (DE-588)4140988-7 gnd Hall-Polynom (DE-588)4158856-3 gnd Endliche Gruppe (DE-588)4014651-0 gnd Symmetrische Funktion (DE-588)4342453-3 gnd |
| subject_GND | (DE-588)4140988-7 (DE-588)4158856-3 (DE-588)4014651-0 (DE-588)4342453-3 |
| title | Symmetric functions and Hall polynomials |
| title_auth | Symmetric functions and Hall polynomials |
| title_exact_search | Symmetric functions and Hall polynomials |
| title_full | Symmetric functions and Hall polynomials I. G. Macdonald |
| title_fullStr | Symmetric functions and Hall polynomials I. G. Macdonald |
| title_full_unstemmed | Symmetric functions and Hall polynomials I. G. Macdonald |
| title_short | Symmetric functions and Hall polynomials |
| title_sort | symmetric functions and hall polynomials |
| topic | Algebraïsche groepen gtt Fonctions symétriques ram Groupes abéliens ram Groupes finis ram Symmetrische groepen gtt Abelian groups Finite groups Hall polynomials Symmetric functions Abelsche Gruppe (DE-588)4140988-7 gnd Hall-Polynom (DE-588)4158856-3 gnd Endliche Gruppe (DE-588)4014651-0 gnd Symmetrische Funktion (DE-588)4342453-3 gnd |
| topic_facet | Algebraïsche groepen Fonctions symétriques Groupes abéliens Groupes finis Symmetrische groepen Abelian groups Finite groups Hall polynomials Symmetric functions Abelsche Gruppe Hall-Polynom Endliche Gruppe Symmetrische Funktion |
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