The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford University Press
2005
|
| Schriftenreihe: | Oxford lecture series in mathematics and its applications
29 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xi, 138 p. 24 cm |
| ISBN: | 0198530684 |
Internformat
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| 650 | 4 | |a Yang-Baxter equation | |
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| 650 | 4 | |a Yang-Baxter equation | |
| 650 | 4 | |a Representations of groups | |
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Datensatz im Suchindex
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| adam_text | THE DYNAMICAL YANG-BAXTER EQUATION, REPRESENTATION THEORY, AND QUANTUM
INTEGRABLE SYSTEMS PAVEL ETINGOF AND FREDERIC LATOUR OXPORD UNIVERSITY
PRESS CONTENTS 1 INTRODUCTION 1 1.1 THE QUANTUM DYNAMICAL YANG*BAXTER
EQUATION 1 1.1.1 THE EQUATION 1 1.1.2 EXAMPLES OF SOLUTIONS OF QDYBE 1
1.1.3 THE QDYBE WITH SPECTRAL PARAMETER 2 1.1.4 TENSOR CATEGORY OF
REPRESENTATIONS 2 1.1.5 GAUGE TRANSFORMATIONS AND CLASSIFICATION 3 1.1.6
DYNAMICAL QUANTUM GROUPS 3 1.1.7 THE CLASSICAL DYNAMICAL YANG-BAXTER
EQUATION 4 1.1.8 EXAMPLES OF SOLUTIONS OF CDYBE 5 1.1.9 CLASSIFICATION
OF SOLUTIONS FOR CDYBE 5 1.2 THE FUSION AND EXCHANGE CONSTRUCTION 6
1.2.1 INTERTWINING OPERATORS 6 1.2.2 THE FUSION AND EXCHANGE OPERATORS 7
1.2.3 FUSION AND EXCHANGE FOR QUANTUM GROUPS 7 1.2.4 THE ABRR EQUATION 8
1.2.5 THE UNIVERSAL FUSION OPERATOR 8 1.2.6 THE DYNAMICAL TWIST EQUATION
9 1.3 TRACES OF INTERTWINERS AND MACDONALD FUNCTIONS 9 1.3.1 TRACE
FUNCTIONS 9 1.3.2 COMMUTING DIFFERENCE OPERATORS 10 1.3.3 DIFFERENCE
EQUATIONS FOR THE TRACE FUNCTIONS 10 1.3.4 MACDONALD FUNCTIONS 10 1.3.5
DYNAMICAL WEYL GROUPS 12 2 BACKGROUND MATERIAL 15 2.1 FACTS ABOUT 5(2 15
2.2 SEMISIMPLE FINITE-DIMENSIONAL LIE ALGEBRAS AND ROOTS 16 2.3 INNER
PRODUCT ON A SIMPLE LIE ALGEBRA 17 2.4 CHEVALLEY GENERATORS 18 2.5
REPRESENTATIONS OF FINITE-DIMENSIONAL SEMISIMPLE LIE ALGEBRAS 19 2.6
IRREDUCIBLE HIGHEST WEIGHT MODULES; SHAPOVALOV FORM 21 3 INTERTWINERS,
FUSION AND EXCHANGE OPERATORS FOR LIE ALGEBRAS 26 3.1 INTERTWINING
OPERATORS 26 3.2 THE FUSION OPERATOR 27 3.3 THE DYNAMICAL TWIST EQUATION
1 28 3.4 THE EXCHANGE OPERATOR 29 3.5 THE ABRR EQUATION 34 CONTENTS 3.6
THE UNIVERSAL FUSION AND EXCHANGE OPERATORS 38 QUANTUM GROUPS 40 4.1
HOPF ALGEBRAS 40 4.2 REPRESENTATIONS OF HOPF ALGEBRAS 41 4.3 THE QUANTUM
GROUP ILQ (SL 2 ) 42 4.4 THE QUANTUM GROUP ILQ (FL) 43 4.5 PBWFORILQTE)
44 4.6 THE HOPF ALGEBRA STRUCTURE ON ILQ (FL) 45 4.7 REPRESENTATION
THEORY OF IIQ (G) 46 4.8 FORMAL VERSION OF QUANTUM GROUPS 47 4.9
QUASI-TRIANGULAR HOPF ALGEBRAS 48 4.10 QUASI-TRIANGULAR HOPF ALGEBRAS
AND REPRESENTATION THEORY 50 4.11 QUASI-TRIANGULARITY AND ILQ (G) 53
4.12 TWISTING 55 4.13 QUASI-CLASSICAL LIMIT FOR THE QYBE 57 4.14
QUASI-CLASSICAL LIMIT FOR THE QDYBE 58 INTERTWINERS, FUSION AND EXCHANGE
OPERATORS FOR ILQ(G) 61 5.1 FUSION OPERATOR FOR ILQ (G) 61 5.2 EXCHANGE
OPERATOR FOR HQ (G) 63 5.3 THE ABRR EQUATION FOR IIQ(0) 64 5.4
QUASI-CLASSICAL LIMIT FOR ABRR EQUATION FOR ILQ (G) 65 DYNAMICAL
R-MATRICES AND INTEGRABLE SYSTEMS 70 6.1 CLASSICAL MECHANICS VS. QUANTUM
MECHANICS 70 6.2 TRANSFER MATRIX CONSTRUCTION 71 6.3 DYNAMICAL TRANSFER
MATRIX CONSTRUCTION 72 TRACES OF INTERTWINERS FOR ILQ (G) 78 7.1
GENERALIZED MACDONALD-RUIJSENAARS OPERATORS 78 7.2 CONSTRUCTION OF F V
(A, /X) 80. 7.3 QUANTUM SPIN CALOGERO-MOSER HAMILTONIAN 80 7.4 F V
( ,(J,)FOTSL 2 85 7.5 CENTER OF ILQ (G) AND QUANTUM TRACES 88 7.6 THE
FUNCTIONS Z V AND X V 92 7.7 THE FUNCTION G 97 7.8 MACDONALD-RUIJSENAARS
EQUATIONS 107 7.9 DUAL MACDONALD-RUIJSENAARS EQUATIONS 107 7.10 THE
SYMMETRY IDENTITY 112 TRACES OF FNTERTWINERS AND MACDONALD POLYNOMIALS
114 8.1 MACDONALD POLYNOMIALS 114 8.2 VECTOR-VALUED CHARACTERS 118
DYNAMICAL WEYL GROUP 127 9.1 DYNAMICAL WEYL GROUP (FOR Q * SL Z ) 127
CONTENTS XI 9.2 DYNAMICAL WEYL GROUP (FOR ANY FINITE-DIM, SIMPLE Q) 131
REFERENCES 135 INDEX 138
|
| adam_txt |
THE DYNAMICAL YANG-BAXTER EQUATION, REPRESENTATION THEORY, AND QUANTUM
INTEGRABLE SYSTEMS PAVEL ETINGOF AND FREDERIC LATOUR OXPORD UNIVERSITY
PRESS CONTENTS 1 INTRODUCTION 1 1.1 THE QUANTUM DYNAMICAL YANG*BAXTER
EQUATION 1 1.1.1 THE EQUATION 1 1.1.2 EXAMPLES OF SOLUTIONS OF QDYBE 1
1.1.3 THE QDYBE WITH SPECTRAL PARAMETER 2 1.1.4 TENSOR CATEGORY OF
REPRESENTATIONS 2 1.1.5 GAUGE TRANSFORMATIONS AND CLASSIFICATION 3 1.1.6
DYNAMICAL QUANTUM GROUPS 3 1.1.7 THE CLASSICAL DYNAMICAL YANG-BAXTER
EQUATION 4 1.1.8 EXAMPLES OF SOLUTIONS OF CDYBE 5 1.1.9 CLASSIFICATION
OF SOLUTIONS FOR CDYBE 5 1.2 THE FUSION AND EXCHANGE CONSTRUCTION 6
1.2.1 INTERTWINING OPERATORS 6 1.2.2 THE FUSION AND EXCHANGE OPERATORS 7
1.2.3 FUSION AND EXCHANGE FOR QUANTUM GROUPS 7 1.2.4 THE ABRR EQUATION 8
1.2.5 THE UNIVERSAL FUSION OPERATOR 8 1.2.6 THE DYNAMICAL TWIST EQUATION
9 1.3 TRACES OF INTERTWINERS AND MACDONALD FUNCTIONS 9 1.3.1 TRACE
FUNCTIONS 9 1.3.2 COMMUTING DIFFERENCE OPERATORS 10 1.3.3 DIFFERENCE
EQUATIONS FOR THE TRACE FUNCTIONS 10 1.3.4 MACDONALD FUNCTIONS 10 1.3.5
DYNAMICAL WEYL GROUPS 12 2 BACKGROUND MATERIAL 15 2.1 FACTS ABOUT 5(2 15
2.2 SEMISIMPLE FINITE-DIMENSIONAL LIE ALGEBRAS AND ROOTS 16 2.3 INNER
PRODUCT ON A SIMPLE LIE ALGEBRA 17 2.4 CHEVALLEY GENERATORS 18 2.5
REPRESENTATIONS OF FINITE-DIMENSIONAL SEMISIMPLE LIE ALGEBRAS 19 2.6
IRREDUCIBLE HIGHEST WEIGHT MODULES; SHAPOVALOV FORM 21 3 INTERTWINERS,
FUSION AND EXCHANGE OPERATORS FOR LIE ALGEBRAS 26 3.1 INTERTWINING
OPERATORS 26 3.2 THE FUSION OPERATOR 27 3.3 THE DYNAMICAL TWIST EQUATION
1 28 3.4 THE EXCHANGE OPERATOR 29 3.5 THE ABRR EQUATION 34 CONTENTS 3.6
THE UNIVERSAL FUSION AND EXCHANGE OPERATORS 38 QUANTUM GROUPS 40 4.1
HOPF ALGEBRAS 40 4.2 REPRESENTATIONS OF HOPF ALGEBRAS 41 4.3 THE QUANTUM
GROUP ILQ (SL 2 ) 42 4.4 THE QUANTUM GROUP ILQ (FL) 43 4.5 PBWFORILQTE)
44 4.6 THE HOPF ALGEBRA STRUCTURE ON ILQ (FL) 45 4.7 REPRESENTATION
THEORY OF IIQ (G) 46 4.8 FORMAL VERSION OF QUANTUM GROUPS 47 4.9
QUASI-TRIANGULAR HOPF ALGEBRAS 48 4.10 QUASI-TRIANGULAR HOPF ALGEBRAS
AND REPRESENTATION THEORY 50 4.11 QUASI-TRIANGULARITY AND ILQ (G) 53
4.12 TWISTING 55 4.13 QUASI-CLASSICAL LIMIT FOR THE QYBE 57 4.14
QUASI-CLASSICAL LIMIT FOR THE QDYBE 58 INTERTWINERS, FUSION AND EXCHANGE
OPERATORS FOR ILQ(G) 61 5.1 FUSION OPERATOR FOR ILQ (G) 61 5.2 EXCHANGE
OPERATOR FOR HQ (G) 63 5.3 THE ABRR EQUATION FOR IIQ(0) 64 5.4
QUASI-CLASSICAL LIMIT FOR ABRR EQUATION FOR ILQ (G) 65 DYNAMICAL
R-MATRICES AND INTEGRABLE SYSTEMS 70 6.1 CLASSICAL MECHANICS VS. QUANTUM
MECHANICS 70 6.2 TRANSFER MATRIX CONSTRUCTION 71 6.3 DYNAMICAL TRANSFER
MATRIX CONSTRUCTION 72 TRACES OF INTERTWINERS FOR ILQ (G) 78 7.1
GENERALIZED MACDONALD-RUIJSENAARS OPERATORS 78 7.2 CONSTRUCTION OF F V
(A, /X) 80. 7.3 QUANTUM SPIN CALOGERO-MOSER HAMILTONIAN 80 7.4 F V
(\,(J,)FOTSL 2 85 7.5 CENTER OF ILQ (G) AND QUANTUM TRACES 88 7.6 THE
FUNCTIONS Z V AND X V 92 7.7 THE FUNCTION G 97 7.8 MACDONALD-RUIJSENAARS
EQUATIONS 107 7.9 DUAL MACDONALD-RUIJSENAARS EQUATIONS 107 7.10 THE
SYMMETRY IDENTITY 112 TRACES OF FNTERTWINERS AND MACDONALD POLYNOMIALS
114 8.1 MACDONALD POLYNOMIALS 114 8.2 VECTOR-VALUED CHARACTERS 118
DYNAMICAL WEYL GROUP 127 9.1 DYNAMICAL WEYL GROUP (FOR Q * SL Z ) 127
CONTENTS XI 9.2 DYNAMICAL WEYL GROUP (FOR ANY FINITE-DIM, SIMPLE Q) 131
REFERENCES 135 INDEX 138 |
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| id | DE-604.BV021510750 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T14:18:44Z |
| indexdate | 2024-07-09T20:37:28Z |
| institution | BVB |
| isbn | 0198530684 |
| language | English |
| lccn | 2005280920 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014727376 |
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| physical | xi, 138 p. 24 cm |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Oxford University Press |
| record_format | marc |
| series | Oxford lecture series in mathematics and its applications |
| series2 | Oxford lecture series in mathematics and its applications |
| spelling | Etingof, Pavel 1969- Verfasser (DE-588)133258858 aut The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems Pavel Etingof and Frédéric Latour Oxford Oxford University Press 2005 xi, 138 p. 24 cm txt rdacontent n rdamedia nc rdacarrier Oxford lecture series in mathematics and its applications 29 Includes bibliographical references and index Kwantummechanica gtt Representatie (wiskunde) gtt Yang-Baxter equation Yang-Baxter-vergelijkingen gtt Representations of groups Quantum groups Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Integrables System (DE-588)4114032-1 gnd rswk-swf Yang-Baxter-Gleichung (DE-588)4291478-4 gnd rswk-swf Quantengruppe (DE-588)4252437-4 gnd rswk-swf Yang-Baxter-Gleichung (DE-588)4291478-4 s Darstellungstheorie (DE-588)4148816-7 s Quantengruppe (DE-588)4252437-4 s Integrables System (DE-588)4114032-1 s b DE-604 Latour, Frederic Sonstige oth Oxford lecture series in mathematics and its applications 29 (DE-604)BV009910017 29 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014727376&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Etingof, Pavel 1969- The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems Oxford lecture series in mathematics and its applications Kwantummechanica gtt Representatie (wiskunde) gtt Yang-Baxter equation Yang-Baxter-vergelijkingen gtt Representations of groups Quantum groups Darstellungstheorie (DE-588)4148816-7 gnd Integrables System (DE-588)4114032-1 gnd Yang-Baxter-Gleichung (DE-588)4291478-4 gnd Quantengruppe (DE-588)4252437-4 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4114032-1 (DE-588)4291478-4 (DE-588)4252437-4 |
| title | The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems |
| title_auth | The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems |
| title_exact_search | The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems |
| title_exact_search_txtP | The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems |
| title_full | The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems Pavel Etingof and Frédéric Latour |
| title_fullStr | The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems Pavel Etingof and Frédéric Latour |
| title_full_unstemmed | The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems Pavel Etingof and Frédéric Latour |
| title_short | The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems |
| title_sort | the dynamical yang baxter equation representation theory and quantum integrable systems |
| topic | Kwantummechanica gtt Representatie (wiskunde) gtt Yang-Baxter equation Yang-Baxter-vergelijkingen gtt Representations of groups Quantum groups Darstellungstheorie (DE-588)4148816-7 gnd Integrables System (DE-588)4114032-1 gnd Yang-Baxter-Gleichung (DE-588)4291478-4 gnd Quantengruppe (DE-588)4252437-4 gnd |
| topic_facet | Kwantummechanica Representatie (wiskunde) Yang-Baxter equation Yang-Baxter-vergelijkingen Representations of groups Quantum groups Darstellungstheorie Integrables System Yang-Baxter-Gleichung Quantengruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014727376&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009910017 |
| work_keys_str_mv | AT etingofpavel thedynamicalyangbaxterequationrepresentationtheoryandquantumintegrablesystems AT latourfrederic thedynamicalyangbaxterequationrepresentationtheoryandquantumintegrablesystems |