The theory of group characters and matrix representations of groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
AMS Chelsea Publ.
2006
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Originally publ.: Oxford : Clarendon Press, 1950. - Literaturverz. S. [301] - 307 |
| Beschreibung: | VIII, 310 S. |
| ISBN: | 0821840673 |
Internformat
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| 245 | 1 | 0 | |a The theory of group characters and matrix representations of groups |c Dudley E. Littlewood |
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Datensatz im Suchindex
| _version_ | 1804142567615365120 |
|---|---|
| adam_text | THE THEORY OF GROUP CHARACTERS AND MATRIX REPRESENTATIONS OF GROUPS
SECOND EDITION DUDLEY E. LITTLEWOOD AMS CHELSEA PUBLISHING AMERICAN
MATHEMATICAL SOCIETY * PROVIDENCE, RHODE ISLAND CONTENTS I. MATRICES
1.1. LINEAR TRANSFORMATIONS . . . . . . 1 1.2. MATRICES . . . . . . . .
2 1.3. THE TRANSFORM OF A MATRIX . . . . . 4 1.4. RECTANGULAR MATRICES
AND VECTORS . . . . 5 1.5. THE CHARACTERISTIC EQUATION OF A MATRIX . . .
. 6 1.6. THE CLASSICAL CANONICAL FORM OF A MATRIX . . . . 7 1.7. THE
CLASSICAL CANONICAL FORM; MULTIPLE CHARACTERISTIC ROOTS . 8 1.8. VARIOUS
PROPERTIES OF MATRICES . . . . . 1 4 1.9. UNITARY AND ORTHOGONAL
MATRICES . . . . . 1 5 II. ALGEBRAS 2.1. DEFINITION OF AN ALGEBRA OVER
THE COMPLEX NUMBERS . . 22 2.2. CHANGE OF BASIS AND THE REGULAR MATRIX
REPRESENTATION . . 23 2.3. SIMPLE MATRIX ALGEBRAS . . . . . . 2 5 2.4.
EXAMPLES OF ASSOCIATIVE ALGEBRAS . . . . . 2 5 2.5. LINEAR SETS AND
SUB-ALGEBRAS . . . . . 2 6 2.6. MODULUS, IDEMPOTENT AND NILPOTENT
ELEMENTS . . . 2 6 2.7. THE REDUCED CHARACTERISTIC EQUATION . . . . 2 7
2.8. REDUCTION OF AN ALGEBRA RELATIVE TO AN IDEMPOTENT . . 29 2.9. THE
TRACE OF AN ELEMENT . . . . . . 3 1 III. GROUPS 3.1. DEFINITION OF A
GROUP . . . . . . 3 2 3.2. SUBGROUPS . . . . . . . 33 3.3. EXAMPLES OF
GROUPS . . . . . . 3 4 3.4. PERMUTATION GROUPS . . . . . . 3 6 3.5. THE
ALTERNATING GROUP . . . . . . 3 7 3.6. CLASSES OF CONJUGATE ELEMENTS . .
. * . 3 8 3.7. CONJUGATE AND SELF-CONJUGATE SUBGROUPS . . . . 4 0 3.8.
THE REPRESENTATIONS OF AN ABSTRACT GROUP AS A PERMUTATION GROUP . 41 IV.
THE FROBENIUS ALGEBRA 4.1. GROUPS AND ALGEBRAS . . . . . . 4 3 4.2. THE
GROUP CHARACTERS . . . . . . 4 5 4.3. MATRIX REPRESENTATIONS AND GROUP
MATRICES . . . 4 8 4.4. CHARACTERISTIC UNITS . . . . . . 5 6 4.5. THE
RELATIONS BETWEEN THE CHARACTERS OF A GROUP AND THOSE OF A SUBGROUP . .
. . . . . 5 7 V. THE SYMMETRIC GROUP 5.1. PARTITIONS . . . . . . . 69
5.2. FROBENIUS S FORMULA FOR THE CHARACTERS OF THE SYMMETRIC GROUP . 61
5.3. CHARACTERS AND LATTICES . . . . . . 6 7 5.4. PRIMITIVE
CHARACTERISTIC UNITS AND YOUNG TABLEAUX . . 7 1 CONTENTS VII VI.
IMMANANTS AND ^-FUNCTIONS 6.1. IMMANANTS OF A MATRIX . . . . . . 8 1
6.2. SCHUR FUNCTIONS . . . . . . . 8 2 6.3. PROPERTIES OF . 8 7 6.4.
GENERATING FUNCTIONS AND FURTHER PROPERTIES OF ^-FUNCTIONS . 98 6.5.
RELATIONS BETWEEN IMMANANTS AND IS-FUNCTIONS . . .118 VII. S-FUNCTIONS
OF SPECIAL SERIES 7.1. THE FUNCTION *(G, X) . . . . .122 7.2. THE
FUNCTIONS (L-X)~ N AND (L-AJ ) * * * * .126 7.3. /S-FUNCTIONS ASSOCIATED
WITH F(X T ) . . . .131 VIII. THE CALCULATION OF THE CHARACTERS OF THE
SYMMETRIC GROUP 8.1. FROBENIUS S FORMULA . . . . . . 137 IS-FUNCTIONS OF
SPECIAL SERIES . . . . .138 RECURRENCE RELATIONS . . . . . .140
CONGRUENCES . . . . . . .142 CLASSES FOR WHICH THE ORDERS OF THE CYCLES
HAVE A COMMON FACTOR * 143 GRAPHS AND LATTICES . . . . . .146 ORTHOGONAL
PROPERTIES . . . . . . 146 IX. GROUP CHARACTERS AND THE STRUCTURE OF
GROUPS 9.1. THE COMPOUND CHARACTER ASSOCIATED WITH A SUBGROUP . . 147
9.2. DEDUCTION OF THE CHARACTERS OF A SUBGROUP FROM THOSE OF THE GROUP
150 9.3. DETERMINATION OF SUBGROUPS: NECESSARY CRITERIA THAT A COM-
POUND CHARACTER SHOULD CORRESPOND TO A PERMUTATION REPRESENTA- TION OF
THE GROUP . . . . . . 165 9.4. THE PROPERTIES OF GROUPS AND CHARACTER
TABLES . . . 159 9.5. TRANSITIVITY . . . . . . .164 9.6. INVARIANT
SUBGROUPS . . . . . . 171 X. CONTINUOUS MATRIX GROUPS AND INVARIANT
MATRICES 10.1. INVARIANT MATRICES . . . . . . 178 10.2. THE CLASSICAL
CANONICAL FORM OF AN INVARIANT MATRIX . . 193 10.3. APPLICATION TO
INVARIANT THEORY . . . . 203 XI. GROUPS OF UNITARY MATRICES 11.1.
INTRODUCTORY . . . . . . .210 11.2. FUNDAMENTAL FORMULA FOR INTEGRATION
OVER THE GROUP MANIFOLD . 211 11.3. SIMPLIFICATION OF INTEGRATION
FORMULAE FOR CLASS FUNCTIONS . 217 11.4. VERIFICATION OF THE ORTHOGONAL
PROPERTIES OF THE CHARACTERS OF THE UNITARY GROUP . . . . . . 222 11.5.
ORTHOGONAL MATRICES AND THE ROTATION GROUPS . . . 223 11.6. RELATIONS
BETWEEN THE CHARACTERS OF D AND D . . .225 VIII CONTENTS 11.7.
INTEGRATION FORMULAE CONNECTED WITH D AND D . . .227 11.8. THE
CHARACTERS OF THE ORTHOGONAL GROUP . . . . 233 11.9. ALTERNATIVE FORMS
FOR THE CHARACTERS OF THE ORTHOGONAL GROUP . 238 11.10. THE DIFFERENCE
CHARACTERS OF THE ROTATION GROUP . . 245 11.11. THE SPIN REPRESENTATIONS
OF THE ORTHOGONAL GROUP . . 248 11.12. COMPLEX ORTHOGONAL MATRICES AND
GROUPS OF MATRICES WITH A QUADRATIC INVARIANT . . . . . .260 APPENDIX
TABLES OF CHARACTERS OF THE SYMMETRIC GROUPS . . . 265 TABLES OF
CHARACTERS OF TRANSITIVE SUBGROUPS. ALTERNATING GROUPS . 272 GENERAL
CYCLIC GROUP OF ORDER N . . . . .273 OTHER TRANSITIVE SUBGROUPS . . . .
. . 273 SOME RECENT DEVELOPMENTS . . . . . . 285 BIBLIOGRAPHY . . . . .
. .301 SUPPLEMENTARY BIBLIOGRAPHY . . . .306 INDEX . . . . . . * -309
CORRIGENDUM P. 23. THE REGULAR MATRIX REPRESENTATION THIS REPRESENTATION
WILL NOT BE AIMPLY ISOMORPHIC IF THERE EXISTS AN ELEMENT X OF THE
ALGEBRA FOR WHICH OX = 0 FOR ALL O OF THE ALGEBRA. THE CORRESPONDING
MATRIX X WOULD BE IDENTICALLY ZERO. A SIMPLY ISOMORPHIC REPRESENTATION,
HOWEVER, MAY BE OBTAINED IN ANY CASE BY ADJOINING A MODULUS TO THE
ALGEBRA BEFORE OBTAINING THE REGULAR REPRESENTATION.
|
| any_adam_object | 1 |
| author | Littlewood, Dudley Ernest 1903-1979 |
| author_GND | (DE-588)172228344 |
| author_facet | Littlewood, Dudley Ernest 1903-1979 |
| author_role | aut |
| author_sort | Littlewood, Dudley Ernest 1903-1979 |
| author_variant | d e l de del |
| building | Verbundindex |
| bvnumber | BV025414553 |
| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)846017054 (DE-599)BVBBV025414553 |
| dewey-full | 512.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.22 |
| dewey-search | 512.22 |
| dewey-sort | 3512.22 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV025414553 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:33:49Z |
| institution | BVB |
| isbn | 0821840673 |
| language | English |
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| owner_facet | DE-11 |
| physical | VIII, 310 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | AMS Chelsea Publ. |
| record_format | marc |
| spelling | Littlewood, Dudley Ernest 1903-1979 Verfasser (DE-588)172228344 aut The theory of group characters and matrix representations of groups Dudley E. Littlewood 2. ed. Providence, RI AMS Chelsea Publ. 2006 VIII, 310 S. txt rdacontent n rdamedia nc rdacarrier Originally publ.: Oxford : Clarendon Press, 1950. - Literaturverz. S. [301] - 307 Symmetrische Gruppe (DE-588)4184204-2 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Charakter Gruppentheorie (DE-588)4158438-7 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Unitäre Matrix (DE-588)4385390-0 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 s Gruppentheorie (DE-588)4072157-7 s Symmetrische Gruppe (DE-588)4184204-2 s Unitäre Matrix (DE-588)4385390-0 s DE-604 Darstellungstheorie (DE-588)4148816-7 s 1\p DE-604 Charakter Gruppentheorie (DE-588)4158438-7 s 2\p DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-3033-7 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020034755&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Littlewood, Dudley Ernest 1903-1979 The theory of group characters and matrix representations of groups Symmetrische Gruppe (DE-588)4184204-2 gnd Gruppentheorie (DE-588)4072157-7 gnd Charakter Gruppentheorie (DE-588)4158438-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd Unitäre Matrix (DE-588)4385390-0 gnd Darstellung Mathematik (DE-588)4128289-9 gnd |
| subject_GND | (DE-588)4184204-2 (DE-588)4072157-7 (DE-588)4158438-7 (DE-588)4148816-7 (DE-588)4385390-0 (DE-588)4128289-9 |
| title | The theory of group characters and matrix representations of groups |
| title_auth | The theory of group characters and matrix representations of groups |
| title_exact_search | The theory of group characters and matrix representations of groups |
| title_full | The theory of group characters and matrix representations of groups Dudley E. Littlewood |
| title_fullStr | The theory of group characters and matrix representations of groups Dudley E. Littlewood |
| title_full_unstemmed | The theory of group characters and matrix representations of groups Dudley E. Littlewood |
| title_short | The theory of group characters and matrix representations of groups |
| title_sort | the theory of group characters and matrix representations of groups |
| topic | Symmetrische Gruppe (DE-588)4184204-2 gnd Gruppentheorie (DE-588)4072157-7 gnd Charakter Gruppentheorie (DE-588)4158438-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd Unitäre Matrix (DE-588)4385390-0 gnd Darstellung Mathematik (DE-588)4128289-9 gnd |
| topic_facet | Symmetrische Gruppe Gruppentheorie Charakter Gruppentheorie Darstellungstheorie Unitäre Matrix Darstellung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020034755&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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