Representation theory and harmonic analysis of wreath products of finite groups:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2014
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society lecture note series
410 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027097721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XII, 163 S. graph. Darst. |
| ISBN: | 9781107627857 |
Staff View
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| 245 | 1 | 0 | |a Representation theory and harmonic analysis of wreath products of finite groups |c Tullio Ceccherini-Silberstein ; Fabio Scarabotti ; Filippo Tolli |
| 250 | |a 1. publ. | ||
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| 300 | |a XII, 163 S. |b graph. Darst. | ||
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Record in the Search Index
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 A 985-410 |
|---|---|
| DE-BY-TUM_katkey | 1985229 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040071436843 |
| _version_ | 1821933700937416704 |
| adam_text | Titel: Representation theory and harmonic analysis of wreath products of finite groups
Autor: Ceccherini-Silberstein, Tullio
Jahr: 2014
Contents
Preface page xi
1 General theory 1
1.1 Induced representations 1
1.1.1 Definitions 1
1.1.2 Transitivity and additivity of induction 8
1.1.3 Frobenius character formula 10
1.1.4 Induction and restriction 11
1.1.5 Induced representations and induced operators 14
1.1.6 Frobenius reciprocity 14
1.2 Harmonic analysis on a finite homogeneous space 16
1.2.1 Frobenius reciprocity for permutation representations 16
1.2.2 Spherical functions 22
1.2.3 The other side of Frobenius reciprocity for
permutation representations 34
1.2.4 Gelfand pairs 37
1.3 Clifford theory 41
1.3.1 Clifford correspondence 42
1.3.2 The little group method 49
1.3.3 Semidirect products 50
1.3.4 Semidirect products with an Abelian normal subgroup 51
1.3.5 The affine group over a finite field 52
1.3.6 The finite Heisenberg group 56
2 Wreath products of finite groups and their
representation theory 60
2.1 Basic properties of wreath products of finite groups 60
2.1.1 Definitions 60
vii
viii
Contents
2.1.2 Composition and exponentiation actions 63
2.1.3 Iterated wreath products and their actions on
rooted trees 67
2.1.4 Spherically homogeneous rooted trees and their
automorphism group 69
2.1.5 The finite ultrametric space 70
2.2 Two applications of wreath products to group theory 76
2.2.1 The theorem of Kaloujnine and Krasner 76
2.2.2 Primitivity of the exponentiation action 78
2.3 Conjugacy classes of wreath products 81
2.3.1 A general description of conjugacy classes 82
2.3.2 Conjugacy classes of groups of the form 1 G 86
2.3.3 Conjugacy classes of groups of the form F 1 Sn 89
2.4 Representation theory of wreath products 92
2.4.1 The irreducible representations of wreath products 92
2.4.2 The character and matrix coefficients of the
representation a 95
2.5 Representation theory of groups of the form C2IG 98
2.5.1 Representation theory of the finite lamplighter
group C2 ; C„ 99
2.5.2 Representation theoiy of the hyperoctahedral group
C2iS„ 100
2.6 Representation theory of groups of the form F ï Sn 101
2.6.1 Representation theory of Sm 1 Sn 103
3 Harmonic analysis on some homogeneous spaces of finite
wreath products 104
3.1 Harmonic analysis on the composition of two
permutation representations 104
3.1.1 Decomposition into irreducible representations 104
3.1.2 Spherical matrix coefficients 107
3.2 The generalized Johnson scheme 110
3.2.1 The Johnson scheme 110
3.2.2 The homogeneous space ©/, 112
3.2.3 Two special kinds of tensor product 117
3.2.4 The decomposition of L(©/,) into irreducible
representations 120
3.2.5 The spherical functions 123
3.2.6 The homogeneous space V(r, s) and the associated
Gelfandpair 127
Contents
ix
3.3 Harmonie analysis on exponentiations and on wreath
products of permutation representations 130
3.3.1 Exponentiation and wreath products 130
3.3.2 The case G = Ci and Z trivial 139
3.3.3 The case when L{Y) is multiplicity free 142
3.3.4 Exponentiation of finite Gelfand pairs 144
3.4 Harmonic analysis on finite lamplighter spaces 145
3.4.1 Finite lamplighter spaces 145
3.4.2 Spectral analysis of an invariant operator 148
3.4.3 Spectral analysis of lamplighter graphs 150
3.4.4 The lamplighter on the complete graph 153
References
Index
157
161
|
| any_adam_object | 1 |
| author | Ceccherini-Silberstein, Tullio 1966- Scarabotti, Fabio 1966- Tolli, Filippo 1968- |
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| author_facet | Ceccherini-Silberstein, Tullio 1966- Scarabotti, Fabio 1966- Tolli, Filippo 1968- |
| author_role | aut aut aut |
| author_sort | Ceccherini-Silberstein, Tullio 1966- |
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| classification_tum | MAT 430f MAT 203f |
| ctrlnum | (OCoLC)870197850 (DE-599)GBV755614356 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV041657233 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:51:38Z |
| institution | BVB |
| isbn | 9781107627857 |
| language | English |
| lccn | 2013024946 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027097721 |
| oclc_num | 870197850 |
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| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | XII, 163 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spellingShingle | Ceccherini-Silberstein, Tullio 1966- Scarabotti, Fabio 1966- Tolli, Filippo 1968- Representation theory and harmonic analysis of wreath products of finite groups London Mathematical Society lecture note series aHarmonic analysis aFinite groups Harmonische Analyse (DE-588)4023453-8 gnd Endliche Gruppe (DE-588)4014651-0 gnd Kranzprodukt (DE-588)4165535-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4014651-0 (DE-588)4165535-7 (DE-588)4148816-7 |
| title | Representation theory and harmonic analysis of wreath products of finite groups |
| title_auth | Representation theory and harmonic analysis of wreath products of finite groups |
| title_exact_search | Representation theory and harmonic analysis of wreath products of finite groups |
| title_full | Representation theory and harmonic analysis of wreath products of finite groups Tullio Ceccherini-Silberstein ; Fabio Scarabotti ; Filippo Tolli |
| title_fullStr | Representation theory and harmonic analysis of wreath products of finite groups Tullio Ceccherini-Silberstein ; Fabio Scarabotti ; Filippo Tolli |
| title_full_unstemmed | Representation theory and harmonic analysis of wreath products of finite groups Tullio Ceccherini-Silberstein ; Fabio Scarabotti ; Filippo Tolli |
| title_short | Representation theory and harmonic analysis of wreath products of finite groups |
| title_sort | representation theory and harmonic analysis of wreath products of finite groups |
| topic | aHarmonic analysis aFinite groups Harmonische Analyse (DE-588)4023453-8 gnd Endliche Gruppe (DE-588)4014651-0 gnd Kranzprodukt (DE-588)4165535-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | aHarmonic analysis aFinite groups Harmonische Analyse Endliche Gruppe Kranzprodukt Darstellungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027097721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
| work_keys_str_mv | AT ceccherinisilbersteintullio representationtheoryandharmonicanalysisofwreathproductsoffinitegroups AT scarabottifabio representationtheoryandharmonicanalysisofwreathproductsoffinitegroups AT tollifilippo representationtheoryandharmonicanalysisofwreathproductsoffinitegroups |
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0102 MAT 001z 2001 A 985-410
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