Holdings: The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems

The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems:

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Bibliographic Details
Main Author:	Etingof, Pavel 1969- (Author)
Format:	Book
Language:	English
Published:	Oxford Oxford University Press 2005
Series:	Oxford lecture series in mathematics and its applications 29
Subjects:	Kwantummechanica Representatie (wiskunde) Yang-Baxter equation Yang-Baxter-vergelijkingen Representations of groups Quantum groups Darstellungstheorie Integrables System Yang-Baxter-Gleichung Quantengruppe
Online Access:	Inhaltsverzeichnis
Item Description:	Includes bibliographical references and index
Physical Description:	xi, 138 p. 24 cm
ISBN:	0198530684

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MARC


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Record in the Search Index

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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 YANGBAXTER 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 YANGBAXTER 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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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
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volume_link	(DE-604)BV009910017
work_keys_str_mv	AT etingofpavel thedynamicalyangbaxterequationrepresentationtheoryandquantumintegrablesystems AT latourfrederic thedynamicalyangbaxterequationrepresentationtheoryandquantumintegrablesystems

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