Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
2000
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society: [London Mathematical Society monographs
21 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009025661&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XV, 446 S. |
| ISBN: | 0198502508 |
Staff View
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| 245 | 1 | 0 | |a Characters of finite Coxeter groups and Iwahori-Hecke algebras |c Meinolf Geck and Götz Pfeiffer |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford |b Clarendon Press |c 2000 | |
| 300 | |a XV, 446 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a London Mathematical Society: [London Mathematical Society monographs / New series] |v 21 | |
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Record in the Search Index
| DE-BY-UBR_call_number | 80/SK 260 G294 |
|---|---|
| DE-BY-UBR_katkey | 3042009 |
| DE-BY-UBR_location | UB Lesesaal Mathematik |
| DE-BY-UBR_media_number | 069030339568 |
| _version_ | 1835114465221148673 |
| adam_text | Contents
1 Cartan matrices and finite Coxeter groups 1
1.1 Cartan matrices and reflection groups 4
1.2 Matsumoto s theorem 10
1.3 Cartan matrices of finite type 15
1.4 Coxeter groups of classical type 20
1.5 The longest element 26
1.6 Bibliographical remarks and exercises 33
2 Parabolic subgroups 38
2.1 Distinguished coset representatives 39
2.2 Longest representatives and the coset graph 45
2.3 Coxeter classes 53
2.4 The parabolic table of marks 60
2.5 Bibliographical remarks and exercises 67
3 Conjugacy classes and special elements 73
3.1 Cuspidal classes 74
3.2 The conjugacy graph 79
3.3 Algorithms and reduction theorems 87
3.4 Minimal elements in classical types 91
3.5 Bibliographical remarks and exercises 100
4 The braid monoid and good elements 105
4.1 The braid monoid and the braid group 106
4.2 Divisibility in braid monoids 111
4.3 Good elements in braid monoids 116
4.4 Iwahori Hecke algebras 122
4.5 Invariants of knots and links 127
4.6 Bibliographical remarks and exercises 133
5 Irreducible characters of finite Coxeter groups 137
5.1 Exterior powers of the reflection representation 138
5.2 Macdonald Lusztig Spaltenstein induction 141
5.3 Applications to finite Coxeter groups 148
5.4 The characters of the symmetric group 154
5.5 The characters of Coxeter groups of type B 163
5.6 The characters of Coxeter groups of type D 169
5.7 Bibliographical remarks and exercises 172
xiv Contents
6 Parabolic subgroups and induced characters 177
6.1 Induction of characters in classical types 178
6.2 Central characters in classical types 183
6.3 Characters of parabolic type 190
6.4 Symbols for the classical types 193
6.5 Families and a functions 202
6.6 Bibliographical remarks and exercises 212
7 Representation theory of symmetric algebras 217
7.1 Trace functions 218
7.2 Schur relations and Schur elements 223
7.3 Grothendieck groups and integrality 228
7.4 Specializations and Tits s deformation theorem 234
7.5 Properties of the decomposition map 239
7.6 Bibliographical remarks and exercises 246
8 Iwahori Hecke algebras 250
8.1 Generic Iwahori Hecke algebras 251
8.2 Class polynomials 261
8.3 Iwahori Hecke algebras of dihedral type 267
8.4 Iwahori s theorem 274
8.5 Bibliographical remarks and exercises 281
9 Characters of Iwahori Hecke algebras 286
9.1 Induction from parabolic subalgebras 287
9.2 Character values and the longest element 294
9.3 Splitting fields for Iwahori Hecke algebras 302
9.4 Character values and Schur elements 309
9.5 Bibliographical remarks and exercises 317
10 Character values in classical types 321
10.1 Hoefsmit s matrices 322
10.2 Character values of type A 327
10.3 Character values of type B 332
10.4 Character values of type D 336
10.5 On the generic degrees of the classical types 345
10.6 The Lascoux Leclerc Thibon conjecture 353
10.7 Bibliographical remarks and exercises 357
11 Computing character values and generic degrees 361
11.1 W graphs and representing matrices 362
11.2 W graphs for the irreducible characters of type H4 370
11.3 W graphs for the irreducible characters of type F4 375
11.4 On the computation of the generic degrees 380
Contents xv
11.5 On the computation of character values 383
11.6 Bibliographical remarks and exercises 393
Appendix: Tables for the exceptional types 398
A Coxeter classes and parabolic tables of marks 398
B Good representatives of cuspidal classes 406
C Irreducible characters 411
D Truncated induction 417
E Generic degrees 422
F Blocks at roots of unity 428
References 435
Index 445
|
| any_adam_object | 1 |
| author | Geck, Meinolf ca. 20./21. Jh |
| author_GND | (DE-588)1018524649 |
| author_facet | Geck, Meinolf ca. 20./21. Jh |
| author_role | aut |
| author_sort | Geck, Meinolf ca. 20./21. Jh |
| author_variant | m g mg |
| building | Verbundindex |
| bvnumber | BV013243338 |
| callnumber-first | Q - Science |
| callnumber-label | QA177 |
| callnumber-raw | QA177 |
| callnumber-search | QA177 |
| callnumber-sort | QA 3177 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)247646510 (DE-599)BVBBV013243338 |
| 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 | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV013243338 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:43:48Z |
| institution | BVB |
| isbn | 0198502508 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009025661 |
| oclc_num | 247646510 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-11 DE-824 |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-11 DE-824 |
| physical | XV, 446 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | London Mathematical Society: [London Mathematical Society monographs / New series] Oxford science publications |
| spellingShingle | Geck, Meinolf ca. 20./21. Jh Characters of finite Coxeter groups and Iwahori-Hecke algebras Endliche Gruppe - Charakter <Gruppentheorie> - Coxeter-Gruppe Iwahori-Hecke-Algebra Coxeter-Gruppe (DE-588)4261522-7 gnd Charakter Gruppentheorie (DE-588)4158438-7 gnd Iwahori-Hecke-Algebra (DE-588)4378152-4 gnd |
| subject_GND | (DE-588)4261522-7 (DE-588)4158438-7 (DE-588)4378152-4 |
| title | Characters of finite Coxeter groups and Iwahori-Hecke algebras |
| title_auth | Characters of finite Coxeter groups and Iwahori-Hecke algebras |
| title_exact_search | Characters of finite Coxeter groups and Iwahori-Hecke algebras |
| title_full | Characters of finite Coxeter groups and Iwahori-Hecke algebras Meinolf Geck and Götz Pfeiffer |
| title_fullStr | Characters of finite Coxeter groups and Iwahori-Hecke algebras Meinolf Geck and Götz Pfeiffer |
| title_full_unstemmed | Characters of finite Coxeter groups and Iwahori-Hecke algebras Meinolf Geck and Götz Pfeiffer |
| title_short | Characters of finite Coxeter groups and Iwahori-Hecke algebras |
| title_sort | characters of finite coxeter groups and iwahori hecke algebras |
| topic | Endliche Gruppe - Charakter <Gruppentheorie> - Coxeter-Gruppe Iwahori-Hecke-Algebra Coxeter-Gruppe (DE-588)4261522-7 gnd Charakter Gruppentheorie (DE-588)4158438-7 gnd Iwahori-Hecke-Algebra (DE-588)4378152-4 gnd |
| topic_facet | Endliche Gruppe - Charakter <Gruppentheorie> - Coxeter-Gruppe Iwahori-Hecke-Algebra Coxeter-Gruppe Charakter Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009025661&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV045355493 |
| work_keys_str_mv | AT geckmeinolf charactersoffinitecoxetergroupsandiwahoriheckealgebras AT pfeiffergotz charactersoffinitecoxetergroupsandiwahoriheckealgebras |