Etingof P., Frenkel I., Kirillov A. — Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations :: Электронная библиотека попечительского совета мехмата МГУ

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Etingof P., Frenkel I., Kirillov A. — Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations

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Название: Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations

Авторы: Etingof P., Frenkel I., Kirillov A.

Аннотация:

This book is devoted to mathematical structures arising in conformal field theory and the $q$-deformations. The authors give a self-contained exposition of the theory of Knizhnik-Zamolodchikov equations and related topics. No previous knowledge of physics is required. The text is suitable for a one-semester graduate course.

Язык:

Рубрика: Математика/Алгебра/Квантовые группы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 198

Добавлена в каталог: 26.03.2005

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Предметный указатель

$\beta \gamma$ -system      67
$\beta \gamma$ -system, quantum      180
6j-symbols      95
Asymptotic solution for a difference equation      173
Asymptotic solutionof KZ equations      117
Asymptotic zone      117
Braid group      87
Braided tensor category      86
Cartan matrix      16
Cartan matrix, generalized      21
Cartan matrix, symmetrizable      22 82
Casimir element      19
Casimir element, quantum      92
Central charge      23
Classical r-matrix      45
Cohomology with coefficients in a local system      99
Conformal blocks      183
Connection      97
Connection matrices for difference equations      173
Connection matrices for KZ equations      119
Connection, flat      98
Correlation function      34
Correlation function for quantum affine algebras      150
Coxeter number      19
Coxeter number, dual      19
Drinfeld associator      125
Drinfeld category      124
Drinfeld — Kohno theorem      126
Elliptic quantum group      181
Evaluation homomorphisms      132
Evaluation representation of affine Lie algebras      25
Evaluation representation of quantum affine algebras      134
Exchange matrix for affine Lie algebras      122
Exchange matrix for quantum affine algebras      177
Exchange matrix for quantum groups      94
Fock module      63 68
Free field realization of intertwining operators      73—77
Free field realization of Verma modules      70
Gauss — Manin connection      105
Heisenberg algebra      63 68
Hexagon axiom      86
Highest-weight vector      17
Holonomic system of difference equations      153
Holonomy      98
Homology, relative      107
Homology, singular      99
Hopf algebra      79
Hopf algebra, cocommutative      81
Hopf algebra, quasitriangular      85
Hypergeometric function      53
Hyperplane arrangement      101
Jackson integral      163

Knizhnik — Zamolodchikov equations      35
Knizhnik — Zamolodchikov equations, elliptic      185
Knizhnik — Zamolodchikov equations, operator      32
Knizhnik — Zamolodchikov equations, quantum      151
Knizhnik — Zamolodchikov equations, quantum, modified      156
Knizhnik — Zamolodchikov equations, quantum, operator      149
Knizhnik — Zamolodchikov equations, trigonometric      44
Knizhnik — Zamolodchikov — Bernard equation      185
Level      23
Level of a solution of KZ equations      49
Level, critical      23
Level, generic      24
Lie algebras, affine      20
Lie algebras, extended      22
Lie algebras, Kac — Moody      21
Lie algebras, simple finite-dimensional      15
Lie algebras, simply-laced      16
Local system      98
monodromy      114
Normal ordering      64
Orlik — Solomon algebra      101
Pentagon axiom      86
Pochhammer loop      53
q-hypergeometric function      164
Quantum affine algebra      131
Quantum double      89
Quantum groups      83
Quasimeromorphic function      172
Screening operators      75
Shapovalov form      17
Singular vectors      19
Star-triangle relation      94
Sugawara construcion      26
Universal R-matrix      85
Universal R-matrix for $U_q(\mathfrak{g}_e)$       90
Universal R-matrix for quantum affine algebras      136
Vacuum vector      64
Verma module      17
Verma module for affine Lie algebras      22
Verma module for affine Lie algebras, contragredient      24
Verma module for quantum groups      83
Verma module, contragredient      18
Vertex operator      64
Virasoro algebra      25
Wakimoto module      70
Weight decomposition      17
Weight decomposition for quantum groups      83
Weight subspace      17
Weyl module      23
Yang — Baxter equation with a spectral parameter      137
Yang — Baxter equation, classical      45
Yang — Baxter equation, dynamical      96
Yang — Baxter equation, quantum      87

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