Lie groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
[2013]
|
| Edition: | Second edition |
| Series: | Graduate texts in mathematics
225 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xiii, 551 Seiten Illustrationen, Diagramme |
| ISBN: | 9781461480235 9781493938421 |
Staff View
MARC
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| 100 | 1 | |a Bump, Daniel |d 1952- |e Verfasser |0 (DE-588)110339959 |4 aut | |
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| 264 | 4 | |c © 2013 | |
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 225 | |
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Record in the Search Index
| _version_ | 1804151465873244160 |
|---|---|
| adam_text | Contents
Preface
........................................................
v
Part I Compact Groups
1 Haar
Measure
............................................. 3
2 Schur
Orthogonality
....................................... 7
3
Compact Operators
........................................ 19
4
The Peter-Weyl Theorem
................................. 23
Part II Compact Lie Groups
5
Lie Subgroups of GL(n, C)
................................. 31
6
Vector Fields
.............................................. 39
7
Left-Invariant Vector Fields
............................... 45
8
The Exponential Map
..................................... 51
9
Tensors and Universal Properties
.......................... 57
10
The Universal Enveloping Algebra
......................... 61
11
Extension of Scalars
...................................... 67
12
Representations of sl(2, C)
................................ 71
13
The Universal Cover
...................................... 81
xi
xii Contents
14
The Local Frobenius Theorem
............................ 93
15
Tori
.......................................................101
16
Geodesies and Maximal Tori
...............................109
17
The Weyl Integration Formula
.............................123
18
The Root System
..........................................129
19
Examples of Root Systems
.................................145
20
Abstract Weyl Groups
.....................................157
21
Highest Weight Vectors
....................................169
22
The Weyl Character Formula
..............................177
23
The Fundamental Group
...................................191
Part III Noncompact Lie Groups
24
Complexification
...........................................205
25
Coxeter Groups
...........................................213
26
The
Borei
Subgroup
.......................................227
27
The Bruhat Decomposition
................................243
28
Symmetric Spaces
.........................................257
29
Relative Root Systems
.....................................281
30
Embeddings of Lie Groups
.................................303
31
Spin
.......................................................319
Part IV Duality and Other Topics
32
Mackey Theory
............................................337
33
Characters of GL(n, C)
....................................349
34
Duality Between Sk and GL(n, C)
.........................355
r
Contents
xiii
35
The Jacobi-Trudi Identity
................................365
36 Schur
Polynomials and GL(n, C)
..........................379
37 Schur
Polynomials and Sk
................................387
38
The Cauchy Identity
......................................395
39
Random Matrix Theory
..................................407
40
Symmetric Group Branching Rules and Tableaux
.........419
41
Unitary Branching Rules and Tableaux
....................427
42
Minors of
Toeplitz
Matrices
...............................437
43
The Involution Model for Sk
...............................445
44
Some Symmetric Algebras
.................................455
45
Gelfand Pairs
..............................................461
46 Hecke
Algebras
............................................471
47
The Philosophy of Cusp Forms
............................485
48
Cohomology of Grassmannians
............................517
Appendix: Sage
................................................529
References
.....................................................535
Index
..........................................................545
This book is intended for a one-year graduate course on Lie groups and Lie algebras.
The book goes beyond the representation theory of compact Lie groups, which is
the basis of many texts, and provides a carefully chosen range of material to give the
student the bigger picture. The book is organized to allow different paths through the
material depending on one s interests. This second edition has substantial new material,
including improved discussions of underlying principles, streamlining of some proofs,
and many results and topics that were not in the first edition.
For compact Lie groups, the book covers the Peter-Weyl theorem, Lie algebra, conjugacy
of maximal tori, the Weyl group, roots and weights, Weyl character formula, the
fundamental group and more. The book continues with the study of complex analytic
groups and general noncompact Lie groups, covering the Bruhat decomposition,
Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of
Lie groups and spin. Other topics that are treated are symmetric function theory, the
representation theory of the symmetric group, Frobenius-Schur duality and
GL(«)
χ
GL(m) duality with many applications including some in random matrix theory,
branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs,
Hecke
algebras, the philosophy of cusp forms and the cohomology of Grassmannians. An
appendix introduces the reader to the use of Sage mathematical software for Lie group
computations.
|
| any_adam_object | 1 |
| author | Bump, Daniel 1952- |
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| classification_rvk | SK 340 |
| classification_tum | MAT 225f |
| ctrlnum | (OCoLC)862365378 (DE-599)BVBBV041373938 |
| dewey-full | 512.482 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.482 |
| dewey-search | 512.482 |
| dewey-sort | 3512.482 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV041373938 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:55:15Z |
| institution | BVB |
| isbn | 9781461480235 9781493938421 |
| language | English |
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| physical | xiii, 551 Seiten Illustrationen, Diagramme |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Bump, Daniel 1952- Verfasser (DE-588)110339959 aut Lie groups Daniel Bump Second edition New York, NY Springer [2013] © 2013 xiii, 551 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 225 Lie-Gruppe - Lehrbuch Lie groups Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 s DE-604 Lie-Algebra (DE-588)4130355-6 s Erscheint auch als Online-Ausgabe 978-1-4614-8024-2 Graduate texts in mathematics 225 (DE-604)BV000000067 225 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=026822045&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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=026822045&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Bump, Daniel 1952- Lie groups Graduate texts in mathematics Lie-Gruppe - Lehrbuch Lie groups Lie-Algebra (DE-588)4130355-6 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| subject_GND | (DE-588)4130355-6 (DE-588)4035695-4 |
| title | Lie groups |
| title_auth | Lie groups |
| title_exact_search | Lie groups |
| title_full | Lie groups Daniel Bump |
| title_fullStr | Lie groups Daniel Bump |
| title_full_unstemmed | Lie groups Daniel Bump |
| title_short | Lie groups |
| title_sort | lie groups |
| topic | Lie-Gruppe - Lehrbuch Lie groups Lie-Algebra (DE-588)4130355-6 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| topic_facet | Lie-Gruppe - Lehrbuch Lie groups Lie-Algebra Lie-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026822045&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026822045&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT bumpdaniel liegroups |