Representation theory: a first course
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1996
|
| Edition: | Corr. 3. printing |
| Series: | Graduate texts in mathematics
129 : Readings in mathematics |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 551 S. graph. Darst. |
| ISBN: | 0387974954 3540974954 0387975276 3540975276 |
Staff View
MARC
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| 100 | 1 | |a Fulton, William |d 1939- |e Verfasser |0 (DE-588)136272541 |4 aut | |
| 245 | 1 | 0 | |a Representation theory |b a first course |c William Fulton ; Joe Harris |
| 250 | |a Corr. 3. printing | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1996 | |
| 300 | |a XV, 551 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 129 : Readings in mathematics | |
| 650 | 4 | |a Lie algebras | |
| 650 | 4 | |a Lie groups | |
| 650 | 4 | |a Representations of algebras | |
| 650 | 4 | |a Representations of groups | |
| 650 | 0 | 7 | |a Lie-Gruppe |0 (DE-588)4035695-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Darstellung |g Mathematik |0 (DE-588)4128289-9 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1807501852749594624 |
|---|---|
| adam_text |
CONTENTS
PREFACE
V
USING THIS
BOOK
IX
PART
I:
FINITE
GROUPS
1
1.
REPRESENTATIONS
OF
FINITE
GROUPS
3
§1.1:
DEFINITIONS
3
§1.2:
COMPLETE
REDUCIBILITY;
SCHUR
'
S
LEMMA
5
§1.3:
EXAMPLES:
ABELIAN
GROUPS;
S
3
8
2.
CHARACTERS
12
§2.1:
CHARACTERS
12
§2.2:
THE
FIRST
PROJECTION
FORMULA
AND
ITS
CONSEQUENCES
15
§2.3:
EXAMPLES:
S
4
AND
SI
4
18
§2.4:
MORE
PROJECTION
FORMULAS;
MORE
CONSEQUENCES
21
3.
EXAMPLES;
INDUCED
REPRESENTATIONS;
GROUP
ALGEBRAS;
REAL
REPRESENTATIONS
26
§3.1:
EXAMPLES:
S
5
AND
91
5
26
§3.2:
EXTERIOR
POWERS
OF
THE
STANDARD
REPRESENTATION
OF
S
D
31
§3.3:
INDUCED
REPRESENTATIONS
32
§3.4:
THE
GROUP
ALGEBRA
36
§3.5:
REAL
REPRESENTATIONS
AND
REPRESENTATIONS
OVER
SUBFIELDS
OF
C
39
XII
CONTENTS
4.
REPRESENTATIONS
OF
S
D
:
YOUNG
DIAGRAMS
AND
FROBENIUS
'
S
CHARACTER
FORMULA
44
§4.1:
STATEMENTS
OF
THE
RESULTS
44
§4.2:
IRREDUCIBLE
REPRESENTATIONS
OF
S
D
52
§4.3:
PROOF
OF
FROBENIUS
'
S
FORMULA
54
5.
REPRESENTATIONS
OF
AND
GL
2
(F
4
)
63
§5.1:
REPRESENTATIONS
OF
63
§5.2:
REPRESENTATIONS
OF
GL
2
(F,)
AND
SL
2
(F
4
)
67
6.
WEYL
'
S
CONSTRUCTION
75
§6.1:
SCHUR
FUNCTORS
AND
THEIR
CHARACTERS
75
§6.2:
THE
PROOFS
84
PART
II:
LIE
GROUPS
AND
LIE
ALGEBRAS
89
7.
LIE
GROUPS
93
§7.1:
LIE
GROUPS:
DEFINITIONS
93
§7.2:
EXAMPLES
OF
LIE
GROUPS
95
§7.3:
TWO
CONSTRUCTIONS
101
8.
LIE
ALGEBRAS
AND
LIE
GROUPS
104
§8.1:
LIE
ALGEBRAS:
MOTIVATION
AND
DEFINITION
104
§8.2:
EXAMPLES
OF
LIE
ALGEBRAS
111
§8.3:
THE
EXPONENTIAL
MAP
114
9.
INITIAL
CLASSIFICATION
OF
LIE
ALGEBRAS
121
§9.1:
ROUGH
CLASSIFICATION
OF
LIE
ALGEBRAS
121
§9.2:
ENGEL
'
S
THEOREM
AND
LIE
'
S
THEOREM
125
§9.3:
SEMISIMPLE
LIE
ALGEBRAS
128
§9.4:
SIMPLE
LIE
ALGEBRAS
131
10.
LIE
ALGEBRAS
IN
DIMENSIONS
ONE,
TWO,
AND
THREE
133
§10.1:
DIMENSIONS
ONE
AND
TWO
133
§10.2:
DIMENSION
THREE,
RANK
1
136
§10.3:
DIMENSION
THREE,
RANK
2
139
§10.4:
DIMENSION
THREE,
RANK
3
141
11.
REPRESENTATIONS
OF
SI
2
C
146
§11.1:
THE
IRREDUCIBLE
REPRESENTATIONS
146
§11.2:
A
LITTLE
PLETHYSM
151
§11.3:
A
LITTLE
GEOMETRIC
PLETHYSM
153
CONTENTS
XIII
12.
REPRESENTATIONS
OF
SL
3
C,
PART
I
161
13.
REPRESENTATIONS
OF
SI
3
C,
PART
II:
MAINLY
LOTS
OF
EXAMPLES
175
§13.1:
EXAMPLES
175
§13.2:
DESCRIPTION
OF
THE
IRREDUCIBLE
REPRESENTATIONS
182
§13.3:
A
LITTLE
MORE
PLETHYSM
185
§13.4:
A
LITTLE
MORE
GEOMETRIC
PLETHYSM
189
PART
III:
THE
CLASSICAL
LIE
ALGEBRAS
AND
THEIR
REPRESENTATIONS
195
14.
THE
GENERAL
SET-UP:
ANALYZING
THE
STRUCTURE
AND
REPRESENTATIONS
OF
AN
ARBITRARY
SEMISIMPLE
LIE
ALGEBRA
197
§14.1:
ANALYZING
SIMPLE
LIE
ALGEBRAS
IN
GENERAL
197
§14.2:
ABOUT
THE
KILLING
FORM
206
15.
SL4
CANDSIYYC
211
§15.1:
ANALYZING
SIYYC
211
§15.2:
REPRESENTATIONS
OF
SL
4
C
AND
SIYYC
217
§15.3:
WEYL
'
S
CONSTRUCTION
AND
TENSOR
PRODUCTS
222
§15.4:
SOME
MORE
GEOMETRY
227
§15.5:
REPRESENTATIONS
OF
GLYYC
231
16.
SYMPLECTIC
LIE
ALGEBRAS
238
§16.1:
THE
STRUCTURE
OF
SP
2
YYC
AND
SP
2
YYC
238
§16.2:
REPRESENTATIONS
OF
SP
4
C
244
17.
SP
6
C
AND
SP
2
YYC
253
§17.1:
REPRESENTATIONS
OF
SP
6
C
253
§17.2:
REPRESENTATIONS
OF
SP
2
YYC
IN
GENERAL
259
§17.3:
WEYL
'
S
CONSTRUCTION
FOR
SYMPLECTIC
GROUPS
262
18.
ORTHOGONAL
LIE
ALGEBRAS
267
§18.1:
SO
M
C
AND
SO
M
C
267
§18.2:
REPRESENTATIONS
OF
SO
3
C,
SO
4
C,
AND
SO
5
C
273
19.
SO
6
C,
SO
7
C,
AND
SO
M
C
282
§19.1:
REPRESENTATIONS
OF
SO
6C
282
§19.2:
REPRESENTATIONS
OF
THE
EVEN
ORTHOGONAL
ALGEBRAS
286
§19.3:
REPRESENTATIONS
OF
SO
7
C
292
§19.4:
REPRESENTATIONS
OF
THE
ODD
ORTHOGONAL
ALGEBRAS
294
§19.5:
WEYL
'
S
CONSTRUCTION
FOR
ORTHOGONAL
GROUPS
296
XIV
CONTENTS
20.
SPIN
REPRESENTATIONS
OF
SO
M
C
299
§20.1:
CLIFFORD
ALGEBRAS
AND
SPIN
REPRESENTATIONS
OF
SO
M
C
299
§20.2:
THE
SPIN
GROUPS
SPIN
M
C
AND
SPIN
M
R
307
§20.3:
SPIN
8
C
AND
TRIALITY
312
PART
IV:
LIE
THEORY
317
21.
THE
CLASSIFICATION
OF
COMPLEX
SIMPLE
LIE
ALGEBRAS
319
§21.1:
DYNKIN
DIAGRAMS
ASSOCIATED
TO
SEMISIMPLE
LIE
ALGEBRAS
319
§21.2:
CLASSIFYING
DYNKIN
DIAGRAMS
325
§21.3:
RECOVERING
A
LIE
ALGEBRA
FROM
ITS
DYNKIN
DIAGRAM
330
22.
G
2
AND
OTHER
EXCEPTIONAL
LIE
ALGEBRAS
339
§22.1:
CONSTRUCTION
OF
G
2
FROM
ITS
DYNKIN
DIAGRAM
339
§22.2:
VERIFYING
THAT
G
2
IS
A
LIE
ALGEBRA
346
§22.3:
REPRESENTATIONS
OF
G
2
350
§22.4:
ALGEBRAIC
CONSTRUCTIONS
OF
THE
EXCEPTIONAL
LIE
ALGEBRAS
359
23.
COMPLEX
LIE
GROUPS;
CHARACTERS
366
§23.1:
REPRESENTATIONS
OF
COMPLEX
SIMPLE
GROUPS
366
§23.2:
REPRESENTATION
RINGS
AND
CHARACTERS
375
§23.3:
HOMOGENEOUS
SPACES
382
§23.4:
BRUHAT
DECOMPOSITIONS
395
24.
WEYL
CHARACTER
FORMULA
399
§24.1:
THE
WEYL
CHARACTER
FORMULA
399
§24.2:
APPLICATIONS
TO
CLASSICAL
LIE
ALGEBRAS
AND
GROUPS
403
25.
MORE
CHARACTER
FORMULAS
415
§25.1:
FREUDENTHAL
'
S
MULTIPLICITY
FORMULA
415
§25.2:
PROOF
OF
(WCF);
THE
KOSTANT
MULTIPLICITY
FORMULA
419
§25.3:
TENSOR
PRODUCTS
AND
RESTRICTIONS
TO
SUBGROUPS
424
26.
REAL
LIE
ALGEBRAS
AND
LIE
GROUPS
430
§26.1:
CLASSIFICATION
OF
REAL
SIMPLE
LIE
ALGEBRAS
AND
GROUPS
430
§26.2:
SECOND
PROOF
OF
WEYL
'
S
CHARACTER
FORMULA
440
§26.3:
REAL,
COMPLEX,
AND
QUATERNIONIC
REPRESENTATIONS
444
APPENDICES
451
A.
ON
SYMMETRIC
FUNCTIONS
453
§A.L:
BASIC
SYMMETRIC
POLYNOMIALS
AND
RELATIONS
AMONG
THEM
453
§A.2:
PROOFS
OF
THE
DETERMINANTAL
IDENTITIES
462
§A.3:
OTHER
DETERMINANTAL
IDENTITIES
465
CONTENTS
XV
B.
ON
MULTILINEAR
ALGEBRA
471
§B.L:
TENSOR
PRODUCTS
471
§B.2:
EXTERIOR
AND
SYMMETRIC
POWERS
472
§B.3:
DUALS
AND
CONTRACTIONS
475
C.
ON
SEMISIMPLICITY
478
§C.L:
THE
KILLING
FORM
AND
CARTAN
'
S
CRITERION
478
§C.2:
COMPLETE
REDUCIBILITY
AND
THE
JORDAN
DECOMPOSITION
481
§C.3:
ON
DERIVATIONS
483
D.
CARTAN
SUBALGEBRAS
487
§D.L:
THE
EXISTENCE
OF
CARTAN
SUBALGEBRAS
487
§D.2:
ON
THE
STRUCTURE
OF
SEMISIMPLE
LIE
ALGEBRAS
489
§D.3:
THE
CONJUGACY
OF
CARTAN
SUBALGEBRAS
491
§D.4:
ON
THE
WEYL
GROUP
493
E.
ADO
'
S
AND
LEVI
'
S
THEOREMS
499
§E.L:
LEVI
'
S
THEOREM
499
§E.2:
ADO
'
S
THEOREM
500
F.
INVARIANT
THEORY
FOR
THE
CLASSICAL
GROUPS
504
§F.L:
THE
POLYNOMIAL
INVARIANTS
504
§F.2:
APPLICATIONS
TO
SYMPLECTIC
AND
ORTHOGONAL
GROUPS
511
§F.3:
PROOF
OF
CAPELLI
'
S
IDENTITY
514
HINTS,
ANSWERS,
AND
REFERENCES
516
BIBLIOGRAPHY
536
INDEX
OF
SYMBOLS
543
INDEX
547 |
| any_adam_object | 1 |
| author | Fulton, William 1939- Harris, Joe 1951- |
| author_GND | (DE-588)136272541 (DE-588)112574718 |
| author_facet | Fulton, William 1939- Harris, Joe 1951- |
| author_role | aut aut |
| author_sort | Fulton, William 1939- |
| author_variant | w f wf j h jh |
| building | Verbundindex |
| bvnumber | BV011087621 |
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| callnumber-label | QA176 |
| callnumber-raw | QA176 |
| callnumber-search | QA176 |
| callnumber-sort | QA 3176 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 260 SK 340 |
| classification_tum | MAT 225f MAT 173f MAT 202f |
| ctrlnum | (OCoLC)35115160 (DE-599)BVBBV011087621 |
| 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 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Corr. 3. printing |
| format | Book |
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| id | DE-604.BV011087621 |
| illustrated | Illustrated |
| indexdate | 2024-08-16T00:28:12Z |
| institution | BVB |
| isbn | 0387974954 3540974954 0387975276 3540975276 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007427200 |
| oclc_num | 35115160 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-739 DE-384 DE-91 DE-BY-TUM DE-521 DE-11 DE-91G DE-BY-TUM |
| owner_facet | DE-355 DE-BY-UBR DE-739 DE-384 DE-91 DE-BY-TUM DE-521 DE-11 DE-91G DE-BY-TUM |
| physical | XV, 551 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Fulton, William 1939- Verfasser (DE-588)136272541 aut Representation theory a first course William Fulton ; Joe Harris Corr. 3. printing New York [u.a.] Springer 1996 XV, 551 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 129 : Readings in mathematics Lie algebras Lie groups Representations of algebras Representations of groups Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 s Lie-Algebra (DE-588)4130355-6 s DE-604 Lie-Gruppe (DE-588)4035695-4 s Darstellungstheorie (DE-588)4148816-7 s Gruppe Mathematik (DE-588)4022379-6 s 1\p DE-604 Harris, Joe 1951- Verfasser (DE-588)112574718 aut Graduate texts in mathematics 129 : Readings in mathematics (DE-604)BV000000067 129 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007427200&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fulton, William 1939- Harris, Joe 1951- Representation theory a first course Graduate texts in mathematics Lie algebras Lie groups Representations of algebras Representations of groups Lie-Gruppe (DE-588)4035695-4 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Darstellungstheorie (DE-588)4148816-7 gnd Lie-Algebra (DE-588)4130355-6 gnd Gruppe Mathematik (DE-588)4022379-6 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4128289-9 (DE-588)4148816-7 (DE-588)4130355-6 (DE-588)4022379-6 |
| title | Representation theory a first course |
| title_auth | Representation theory a first course |
| title_exact_search | Representation theory a first course |
| title_full | Representation theory a first course William Fulton ; Joe Harris |
| title_fullStr | Representation theory a first course William Fulton ; Joe Harris |
| title_full_unstemmed | Representation theory a first course William Fulton ; Joe Harris |
| title_short | Representation theory |
| title_sort | representation theory a first course |
| title_sub | a first course |
| topic | Lie algebras Lie groups Representations of algebras Representations of groups Lie-Gruppe (DE-588)4035695-4 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Darstellungstheorie (DE-588)4148816-7 gnd Lie-Algebra (DE-588)4130355-6 gnd Gruppe Mathematik (DE-588)4022379-6 gnd |
| topic_facet | Lie algebras Lie groups Representations of algebras Representations of groups Lie-Gruppe Darstellung Mathematik Darstellungstheorie Lie-Algebra Gruppe Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007427200&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT fultonwilliam representationtheoryafirstcourse AT harrisjoe representationtheoryafirstcourse |