Representations of linear groups an introduction based on examples from physics and number theory
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Wiesbaden
Vieweg
2007
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| Ausgabe: | 1. ed. |
| Schlagworte: | |
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| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV022616076 | ||
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| 005 | 20180514 | ||
| 007 | t| | ||
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| 016 | 7 | |a 984802819 |2 DE-101 | |
| 020 | |a 9783834803191 |c Pb. : ca. EUR 39.90 |9 978-3-8348-0319-1 | ||
| 020 | |a 3834803197 |c Pb. : ca. EUR 39.90 |9 3-8348-0319-7 | ||
| 024 | 3 | |a 9783834803191 | |
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| 100 | 1 | |a Berndt, Rolf |d 1940- |e Verfasser |0 (DE-588)140923950 |4 aut | |
| 245 | 1 | 0 | |a Representations of linear groups |b an introduction based on examples from physics and number theory |c Rolf Berndt |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Wiesbaden |b Vieweg |c 2007 | |
| 300 | |a VIII, 270 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Auch als Internetausgabe | ||
| 650 | 4 | |a Linear algebraic groups | |
| 650 | 4 | |a Matrix groups | |
| 650 | 4 | |a Representations of groups | |
| 650 | 0 | 7 | |a Lineare Gruppe |0 (DE-588)4138778-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Darstellungstheorie |0 (DE-588)4148816-7 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Lineare Gruppe |0 (DE-588)4138778-8 |D s |
| 689 | 0 | 1 | |a Darstellungstheorie |0 (DE-588)4148816-7 |D s |
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| 856 | 4 | 2 | |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=2980273&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-015822212 | |
Datensatz im Suchindex
| DE-19_call_number | 1601/SK 260 B524 |
|---|---|
| DE-19_location | 95 |
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| DE-BY-UBR_katkey | 4395452 |
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| DE-BY-UBR_media_number | 069035627410 |
| _version_ | 1823055316145668096 |
| adam_text | Contents
Introduction
ix
0
Prologue:
Some Groups and their Actions
1
0.1
Several Matrix Groups
............................. 1
0.2
Group Actions
................................. 3
0.3
The Symmetric Group
............................. 5
1
Basic Algebraic Concepts
7
1.1
Linear Representations
............................. 7
1.2
Equivalent Representations
.......................... 9
1.3
First Examples
................................ . 10
1.4
Basic Construction Principles
......................... 14
1.4.1
Sum of Representations
........................ 14
1.4.2
Tensor Product of Representations
.................. 14
1.4.3
The Contragredient Representation
.................. 15
1.4.4
The Factor Representation
...................... 16
1.5
Decompositions
................................. 16
1.6
Characters
.................................... 21
2
Representations of Finite Groups
23
2.1
Characters as Orthonormal Systems
..................... 23
2.2
The Regular Representation
.......................... 27
2.3
Characters as Orthonormal Bases
...................... 28
3
Continuous Representations
31
3.1
Topological and Linear Groups
........................ 31
3.2
The Continuity Condition
........................... 33
3.3
Invariant Measures
............................... 38
3.4
Examples
.................................... 40
4
Representations of Compact Groups
43
4.1
Basic Facts
................................... 43
4.2
The Example
G
=
SU{2)
............................ 48
4.3
The Example
G
=
SO(3)
........................... 52
5
Representations of Abelian Groups
59
5.1
Characters and the Pont
r j
agin Dual
..................... 59
5.2
Continuous Decompositions
.......................... 60
6
The Infinitesimal Method
63
6.1
Lie Algebras and their Representations
.................... 63
6.2
The Lie Algebra of a Linear Group
...................... 67
6.3
Derived Representations
............................ 70
6.4
Unitarily
Integrable
Representations of sl(2,R)
............... 73
6.5
The Examples su(2) and heis(R)
................-....... 82
6.6
Some Structure Theory
............................ 84
6.6.1
Specifications of Groups and Lie Algebras
.............. 85
6.6.2
Structure Theory for Complex
Semisimple
Lie Algebras
...... 89
6.6.3
Structure Theory for Compact Real Lie Algebras
.......... 93
6.6.4
Structure Theory for Noncompact Real Lie Algebras
........ 95
6.6.5
Representations of Highest Weight
.................. 97
6.7
The Example su(3)
............................... 104
7
Induced Representations
117
7.1
The Principle of Induction
........................... 117
7.1.1
Preliminary Approach
......................... 118
7.1.2
Mackey s Approach
........................... 120
7.1.3
Final Approach
............................. 125
7.1.4
Some Questions and two Easy Examples
............... 126
7.2
Unitary Representations of SL(2,R)
. .................... 130
7.3
Unitary Representations of SL(2,C) and of the
Lorentz
Group
....... 143
7.4
Unitary Representations of Semidirect Products
............... 147
7.5
Unitary Representations of the
Poincaré
Group
............... 154
7.6
Induced Representations and Vector Bundles
................ 161
8
Geometric Quantization and the Orbit Method
173
8.1
The Hamiltonian Formalism and its Quantization
.............. 173
8.2
Coadjoint Orbits and Representations
.................... 178
8.2.1
Prequantization
............................. 178
8.2.2
Example: Construction of Line Bundles over
M
=
Ρ
l(C)
..... 181
8.2.3
Quantization
.............................. 184
8.2.4
Coadjoint Orbits and Hamiltonian G-spaces
............. 186
8.2.5
Construction of an Irreducible Unitary Representation by an Orbit
196
8.3
The Examples SU(2) and SL(2, R)
...................... 197
8.4
The Example Heis(R)
............................. 202
8.5
Some Hints Concerning the Jacobi Group
.................. 209
9
Epilogue: Outlook to Number Theory
215
9.1
Theta Functions and the
Heisenberg
Group
................. 216
9.2
Modular Forms and SL(2,R)
......................... 221
9.3
Theta Functions and the Jacobi Group
.................... 236
9.4
Hecke s Theory of L-Functions Associated to Modular Forms
....... 239
9.5
Elements of Algebraic Number Theory and
Hecke
L-Functions
...... 246
9.6
Arithmetic L-Functions
............................ 250
9.7
Summary and Final Reflections
........................ 256
Bibliography
261
Index
266
|
| any_adam_object | 1 |
| author | Berndt, Rolf 1940- |
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| bvnumber | BV022616076 |
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| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)180750215 (DE-599)DNB984802819 |
| dewey-full | 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 |
| dewey-search | 512.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed. |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV022616076 |
| illustrated | Illustrated |
| indexdate | 2025-02-03T17:41:49Z |
| institution | BVB |
| isbn | 9783834803191 3834803197 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015822212 |
| oclc_num | 180750215 |
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| physical | VIII, 270 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Vieweg |
| record_format | marc |
| spellingShingle | Berndt, Rolf 1940- Representations of linear groups an introduction based on examples from physics and number theory Linear algebraic groups Matrix groups Representations of groups Lineare Gruppe (DE-588)4138778-8 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4138778-8 (DE-588)4148816-7 (DE-588)4123623-3 |
| title | Representations of linear groups an introduction based on examples from physics and number theory |
| title_auth | Representations of linear groups an introduction based on examples from physics and number theory |
| title_exact_search | Representations of linear groups an introduction based on examples from physics and number theory |
| title_full | Representations of linear groups an introduction based on examples from physics and number theory Rolf Berndt |
| title_fullStr | Representations of linear groups an introduction based on examples from physics and number theory Rolf Berndt |
| title_full_unstemmed | Representations of linear groups an introduction based on examples from physics and number theory Rolf Berndt |
| title_short | Representations of linear groups |
| title_sort | representations of linear groups an introduction based on examples from physics and number theory |
| title_sub | an introduction based on examples from physics and number theory |
| topic | Linear algebraic groups Matrix groups Representations of groups Lineare Gruppe (DE-588)4138778-8 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Linear algebraic groups Matrix groups Representations of groups Lineare Gruppe Darstellungstheorie Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2980273&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015822212&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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