Representations of compact Lie groups:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
2003
|
| Edition: | 3. printing |
| Series: | Graduate texts in mathematics
98 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 299 - 303 |
| Physical Description: | X, 313 S. Ill. |
| ISBN: | 3540136789 0387136789 |
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Record in the Search Index
| _version_ | 1804133156680368128 |
|---|---|
| adam_text | Contents
CHAPTER I
Lie Groups and Lie Algebras I
1.
The Concept of a Lie Group and the Classical Examples
1
2.
Left-Invariant Vector Fields and One-Parameter Groups
U
3.
The Exponential Map
22
4.
Homogeneous Spaces and Quotient Groups
30
5.
Invariant Integration
40
6.
Clifford Algebras and Spinor Groups
54
CHAPTER II
Elementary Representation Theory
64
1-
Representations
65
2. Semisimple
Modules
72
3.
Linear Algebra and Representations
74
4.
Characters and Orthogonality Relations
77
5.
Representations ofSU(2),SO(3),U(2), and O(3).
84
6.
Real and Quaternionic Representations
93
7.
The Character Ring and the Representation Ring
102
8.
Representations of Abelian Groups
107
9.
Representations of Lie Algebras 111
10.
The Lie Algebra sl(2,C)
1
1S
CHAPTER HI
Representative Functions
123
1.
Algebras of
Representati ve
Functions
123
2.
Some Analysis on Compact Groups
129
3.
The Theorem of Peter and Weyl
133
4.
Applications of the Theorem of Peter and Weyl
136
5.
Generalizations of the Theorem of Peter and Weyl
138
6.
Induced Representations
143
Contents
7.
Tannaka-Kreln Duality
146
8. The
Complexifícation
of Compact Lie Groups
151
CHAPTER IV
The Maximal Torus of a Compact Lie Group
157
1.
Maximal Tori
157
2.
Consequences of the Conjugation Theorem
164
3.
The Maximal Tori and Weyl Groups of the Classical Groups
169
4.
Cartan Subgroups of Nonconnected Compact Groups
176
CHAPTER V
Root Systems
183
1.
The Adjoint Representation and Groups of Rank
1 183
2.
Roots and Weyl Chambers
189
3.
Root Systems
197
4.
Bases and Weyl Chambers
202
5.
Dynkin Diagrams
209
6.
The Roots of the Classical Groups
216
7.
The Fundamental Group, the Center and the
Stiefel
Diagram
223
8.
The Structure of the Compact Groups
232
CHAPTER VI
Irreducible Characters and Weights
239
1.
The Weyl Character Formula
239
2.
The Dominant Weight and the Structure of the Representation Ring
249
3.
The Multiplicities of the Weights of an Irreducible Representation
257
4.
Representations of Real or Quaternionic Type
261
5.
Representations of the Classical Groups
265
6.
Representations of the Spinor Groups
278
7.
Representations of the Orthogonal Groups
292
Bibliography 2
Symbol Index
305
Subject Index 3°7
|
| any_adam_object | 1 |
| author | Bröcker, Theodor 1938- Tom Dieck, Tammo 1938- |
| author_GND | (DE-588)106075284 (DE-588)124473091 |
| author_facet | Bröcker, Theodor 1938- Tom Dieck, Tammo 1938- |
| author_role | aut aut |
| author_sort | Bröcker, Theodor 1938- |
| author_variant | t b tb d t t dt dtt |
| building | Verbundindex |
| bvnumber | BV019705229 |
| classification_rvk | SK 260 SK 340 |
| classification_tum | MAT 202f MAT 225f |
| ctrlnum | (OCoLC)249183460 (DE-599)BVBBV019705229 |
| discipline | Mathematik |
| edition | 3. printing |
| format | Book |
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| id | DE-604.BV019705229 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:04:14Z |
| institution | BVB |
| isbn | 3540136789 0387136789 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013032721 |
| oclc_num | 249183460 |
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| owner | DE-19 DE-BY-UBM DE-11 DE-703 |
| owner_facet | DE-19 DE-BY-UBM DE-11 DE-703 |
| physical | X, 313 S. Ill. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Bröcker, Theodor 1938- Verfasser (DE-588)106075284 aut Representations of compact Lie groups Theodor Bröcker ; Tammo tom Dieck 3. printing New York [u.a.] Springer 2003 X, 313 S. Ill. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 98 Literaturverz. S. 299 - 303 Kompakte Lie-Gruppe - Darstellungstheorie Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Kompakte Gruppe (DE-588)4164840-7 gnd rswk-swf Repräsentation (DE-588)4137492-7 gnd rswk-swf Kompakte Lie-Gruppe (DE-588)4164846-8 gnd rswk-swf Kompakte Lie-Gruppe (DE-588)4164846-8 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Lie-Gruppe (DE-588)4035695-4 s 1\p DE-604 Kompakte Gruppe (DE-588)4164840-7 s 2\p DE-604 Repräsentation (DE-588)4137492-7 s 3\p DE-604 Tom Dieck, Tammo 1938- Verfasser (DE-588)124473091 aut Graduate texts in mathematics 98 (DE-604)BV000000067 98 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013032721&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bröcker, Theodor 1938- Tom Dieck, Tammo 1938- Representations of compact Lie groups Graduate texts in mathematics Kompakte Lie-Gruppe - Darstellungstheorie Darstellungstheorie (DE-588)4148816-7 gnd Lie-Gruppe (DE-588)4035695-4 gnd Kompakte Gruppe (DE-588)4164840-7 gnd Repräsentation (DE-588)4137492-7 gnd Kompakte Lie-Gruppe (DE-588)4164846-8 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4035695-4 (DE-588)4164840-7 (DE-588)4137492-7 (DE-588)4164846-8 |
| title | Representations of compact Lie groups |
| title_auth | Representations of compact Lie groups |
| title_exact_search | Representations of compact Lie groups |
| title_full | Representations of compact Lie groups Theodor Bröcker ; Tammo tom Dieck |
| title_fullStr | Representations of compact Lie groups Theodor Bröcker ; Tammo tom Dieck |
| title_full_unstemmed | Representations of compact Lie groups Theodor Bröcker ; Tammo tom Dieck |
| title_short | Representations of compact Lie groups |
| title_sort | representations of compact lie groups |
| topic | Kompakte Lie-Gruppe - Darstellungstheorie Darstellungstheorie (DE-588)4148816-7 gnd Lie-Gruppe (DE-588)4035695-4 gnd Kompakte Gruppe (DE-588)4164840-7 gnd Repräsentation (DE-588)4137492-7 gnd Kompakte Lie-Gruppe (DE-588)4164846-8 gnd |
| topic_facet | Kompakte Lie-Gruppe - Darstellungstheorie Darstellungstheorie Lie-Gruppe Kompakte Gruppe Repräsentation Kompakte Lie-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013032721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT brockertheodor representationsofcompactliegroups AT tomdiecktammo representationsofcompactliegroups |