Representation theory of symmetric groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
[2017]
|
| Series: | Discrete mathematics and its applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xvi, 666 Seiten Illustrationen |
| ISBN: | 9781498719124 |
Staff View
MARC
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| 100 | 1 | |a Méliot, Pierre-Loïc |d 1985- |e Verfasser |0 (DE-588)1128914883 |4 aut | |
| 245 | 1 | 0 | |a Representation theory of symmetric groups |c Pierre-Loïc Meliot, Université Paris Sud, Orsay, France |
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c [2017] | |
| 264 | 4 | |c © 2017 | |
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| 490 | 0 | |a Discrete mathematics and its applications | |
| 500 | |a Includes bibliographical references and index | ||
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Record in the Search Index
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| adam_text | Contents
Preface xi
I Symmetric groups and symmetric functions 1
1 Representations of finite groups and semisimple algebras 3
1.1 Finite groups and their representations ..................... 3
1.2 Characters and constructions on representations ............ 13
1.3 The non-commutative Fourier transform ...................... 18
1.4 Semisimple algebras and modules ............................ 27
1.5 The double commutant theory .............................. 40
2 Symmetric functions and the Frobenius-Schur isomorphism 49
2.1 Conjugacy classes of the symmetric groups................... 50
2.2 The five bases of the algebra of symmetric functions........ 54
2.3 The structure of graded self-adjoint Hopf algebra........... 69
2.4 The Frobenius-Schur isomorphism............................. 78
2.5 The Schur-Weyl duality...................................... 87
3 Combinatorics of partitions and tableaux 99
3.1 Pieri rules and Mumaghan-Nakayama formula .................. 99
3.2 The Robinson-Schensted-Knuth algorithm..................... 108
3.3 Construction of the irreducible representations ........... 131
3.4 The hook-length formula.................................... 140
II Hecke algebras and their representations 147
4 Hecke algebras and the Brauer-Cartan theory 149
4.1 Coxeter presentation of symmetric groups .................. 151
4.2 Representation theory of algebras ......................... 161
4.3 Brauer-Cartan deformation theory.......................... 173
4.4 Structure of generic and specialized Hecke algebras ....... 183
4.5 Polynomial construction of the q-Specht՝ modules........... 207
5 Characters and dualities for Hecke algebras 217
5.1 Quantum groups and their Hopf algebra structure ........... 218
5.2 Representation theory of the quantum groups............... 230
5.3 Jimbo-Schur-Weyl duality................................... 252
vii
viii Contents
5.4 Iwahori-Hecke duality ....................................... 263
5.5 Hall-Littlewood polynomials and characters of Hecke algebras 272
6 Representations of the Hecke algebras specialized at q = 0 287
6.1 Non-commutative symmetric functions ......................... 289
6.2 Quasi-symmetric functions.................................... 299
6.3 The Hecke-Frobenius-Schur isomorphisms....................... 306
III Observables of partitions 325
7 The Ivanov—Kerov algebra of observables 327
7.1 The algebra of partial permutations ......................... 328
7.2 Coordinates of Young diagrams and their moments.............. 339
7.3 Change of basis in the algebra of observables ............... 347
7.4 Observables and topology of Young diagrams .................. 354
8 The Jucys-Murphy elements 375
8.1 The Gelfand-Tsetlin subalgebra of the symmetric group algebra 375
8.2 Jucys-Murphy elements acting on the Gelfand-Tsetlin basis . . 387
8.3 Observables as symmetric functions of the contents .......... 396
9 Symmetric groups and free probability 401
9.1 Introduction to free probability............................. 402
9.2 Free cumulants of Young diagrams........................... 418
9.3 Transition measures and Jucys-Murphy elements................ 426
9.4 The algebra of admissible set partitions..................... 431
10 The Stanley-Féray formula and Kerov polynomials 451
10.1 New observables of Young diagrams........................ 451
10.2 The Stanley-Féray formula for characters of symmetric groups 464
10.3 Combinatorics of the Kerov polynomials ..................... 479
IV Models of random Young diagrams 499
11 Representations of the infinite symmetric group 501
11.1 Harmonic analysis on the Young graph and extremal characters 502
11.2 The bi-infinite symmetric group and the Olshanski semigroup . 511
11.3 Classification of the admissible representations ........ 527
11.4 Spherical representations and the GNS construction ....... 538
12 Asymptotics of central measures 547
12.1 Free quasi-symmetric functions.............................. 548
12.2 Combinatorics of central measures........................... 562
12.3 Gaussian behavior of the observables .................... 576
Contents ix
13 Asymptotics of Fiancherei and Schur-Weyl measures 595
13.1 The Fiancherei and Schur-Weyl models..................... 596
13.2 Limit shapes of large random Young diagrams.............. 602
13.3 Kerov’s central limit theorem for characters .............. 614
Appendix 629
Appendix A Representation theory of semisimple Lie algebras 631
A.1 Nilpotent, solvable and semisimple algebras................. 631
A.2 Root system of a semisimple complex algebra . ............ 635
A.3 The highest weight theory................................... 641
References 649
Index
661
|
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| dewey-search | 512/.22 |
| dewey-sort | 3512 222 |
| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV044031285 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:41:40Z |
| institution | BVB |
| isbn | 9781498719124 |
| language | English |
| lccn | 016050353 |
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| physical | xvi, 666 Seiten Illustrationen |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | CRC Press |
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| series2 | Discrete mathematics and its applications |
| spelling | Méliot, Pierre-Loïc 1985- Verfasser (DE-588)1128914883 aut Representation theory of symmetric groups Pierre-Loïc Meliot, Université Paris Sud, Orsay, France Boca Raton ; London ; New York CRC Press [2017] © 2017 xvi, 666 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Discrete mathematics and its applications Includes bibliographical references and index Symmetric groups Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Symmetrische Gruppe (DE-588)4184204-2 gnd rswk-swf Symmetrische Gruppe (DE-588)4184204-2 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029438547&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Méliot, Pierre-Loïc 1985- Representation theory of symmetric groups Symmetric groups Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd Symmetrische Gruppe (DE-588)4184204-2 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4184204-2 |
| title | Representation theory of symmetric groups |
| title_auth | Representation theory of symmetric groups |
| title_exact_search | Representation theory of symmetric groups |
| title_full | Representation theory of symmetric groups Pierre-Loïc Meliot, Université Paris Sud, Orsay, France |
| title_fullStr | Representation theory of symmetric groups Pierre-Loïc Meliot, Université Paris Sud, Orsay, France |
| title_full_unstemmed | Representation theory of symmetric groups Pierre-Loïc Meliot, Université Paris Sud, Orsay, France |
| title_short | Representation theory of symmetric groups |
| title_sort | representation theory of symmetric groups |
| topic | Symmetric groups Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd Symmetrische Gruppe (DE-588)4184204-2 gnd |
| topic_facet | Symmetric groups Representations of groups Darstellungstheorie Symmetrische Gruppe |
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