Wakimoto M. — Lectures on Infinite Dimensional Lie Algebra :: Электронная библиотека попечительского совета мехмата МГУ

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Wakimoto M. — Lectures on Infinite Dimensional Lie Algebra

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Название: Lectures on Infinite Dimensional Lie Algebra

Автор: Wakimoto M.

Аннотация:

The representation theory of affine lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. There are three valuable works on it, written by Victor G Kac. This volume begins with a survey and review of the material treated in Kac's books. In particular, modular invariance and conformal invariance are explained in more detail. The book then goes further, dealing with some of the recent topics involving the representation theory of affine lie algebras. Since these topics are important not only in themselves but also in their application to some areas of mathematics and mathematical physics, the book expounds them with examples and detailed calculations.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2002

Количество страниц: 444

Добавлена в каталог: 07.11.2010

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Предметный указатель

-soliton solution      425
-soliton solution (of non-linear Schr $\ddot{o}$ dinger equation)      428
-soliton solution (of KdV equation)      392
$\delta$ -function      175
$\lambda$ -bracket      185
$\mathfrak{h}$ -diagonalizable $\mathfrak{g}$ -module      274
$\overline{\mathfrak{h}}$ -component      10
$\overline{\mathfrak{h}}^{*}$ -component      10
$\tau$ -function      389
2-soliton solution (of KdV equation)      392
Admissible $\mathfrak{g}$ -module      77
Admissible representation      77
Admissible weight      77
Admissible weight $\mu_{y}$       115
Affine C art an matrix      3
Affine Dynkin diagram      3
Affine Lie algebra      3
Affine type (Cartan matrix)      2
Annihilation operator      230 288 291
Asymmetry      355
Asymptotic dimension (of Virasoro module)      252
Bi-multiplicativity      355
Boson-fermion correspondence      236
Branching function      269
Branching function (of tensor product)      275
BRST-complex      300
Canonical central element      9
Casimir element (of finite-dimensional Lie algebra)      27
Casimir element (on adjoint representation)      29
Casimir operator (of affine Lie algebra)      212
Central function      154
Character (of finite group)      154
Character (of highest weight $\mathfrak{g}$ -module)      32
Character (of Virasoro module)      241
Character formula (in terms of maximal weights)      36
Character formula (of integrable highest weight $\mathfrak{g}$ -module)      33
Charge      226 231 288 292
Charge decomposition      235 290
Charge operator      235
Charge variable      235
Charged fermionic field      287
Charged free fermion      225
Classical theta function      59
Clifford algebra      288 291
Co - Dynkin diagram      13
Co-integral form      16
Co-label      5
Co-tier number      5
Coboundary operator $d^{st\pm}_{0}$       299
Coboundary operator $d^{\pm}_{0}$       300
Conformal weight      181
Constant field      197
Coset Virasoro field      233 269 274
Coxeter element      367
Coxeter group      12
Coxeter number      6 366
Creation operator      230 288 291
Current      208
Cyclic element      366
Degree of representation (of finite group)      155
Denominator      33
Denominator identity      33
Derived Lie algebra      274 346
Discrete series (of Virasoro algebra)      243
Dominant co-integral form      16
Dominant integral form      15
Dual Coxeter number      6 366
Dual tier number      5
Dynkin diagram      3
Elementary Schur polynomial      402
Energy      226 231 288 292
Energy momentum field      307
Energy operator      213 217 235 372
Equivalent (of Cartan matrices)      1
Equivalent representation (of finite group)      154
Euler - Poincar $\acute{e}$ characteristics      315
EXPONENT      367
Extended affine Weyl group      18
Extended Weyl group      18
Field      175
Finite part      10
Finite part (of affine Cartan matrix)      10
Finite part of and $\lambda$       10
Finite type (Cartan matrix)      2
Fock representation (of Virasoro algebra)      217
Fock space      217 230
Free bosonic field      215
Free field      357
Fresnel's integral      167
Freudenthal de - Vries strange formula      30
Fundamental alcove      14
Fundamental chamber      14
Fundamental co-integral form      16
Fundamental Co-weight      16
Fundamental imaginaxy root      9
Fundamental integral form      15
Fundamental weight      15
Fusion algebra      163
Fusion algebra (associated to fusion datum)      165
Fusion coefficient      128 320
Fusion datum      162
GCM      1
Generalized Cartan matrix      1
Ghost field      295 307
Growth (of Virasoro module)      252
Heaviside function $Y_{+}$       179 331
Heaviside function $Y_{-}$       219 226
Height      44 366
Heisenberg group      66
Highest component      410
Highest root $\theta$       14 20 25 29 352 366
Highest weight      31
Highest weight $\overline{\mathfrak{h}}$ -module      31
Highest weight module (of Virasoro algebra)      240
Highest weight vector      31
Hirota bilinear differential operator      385
Hirota equation (associated to L( $\Lambda$ ))      393
Homogeneous construction (of basic representation)      352
Homogeneous element      178
Homogeneous Heisenberg algebra      352
Homogeneous realization (of affine Lie algebra)      352

Imaginary root      12
Indecomposable Cartan matrix      2
Indefinite type (Cartan matrix)      2
Integrable highest weight module      32
Integral form      15
Intertwining operator      155
Invariant bilinear form      3
Invariant Hermitian form (on Virasoro module)      242
Isotypic subspace      161
Jacobi triple product identity      33 235
Kac - Moody - Cartan matrix      1
Kac - Moody Lie algebra      2
KdV equation      387
Korteweg-de Vries equation      387
Label      5
Level      17
Lie superalgebra $\mathfrak{gl}(m|n)$       179
Lie superalgebra $\mathfrak{gl}(V)$       179
Lie superalgebra bracket      198
Lie superalgebra End      179
Locality      175
Long root      14
Lower component      410
Maximal weight      35
Metaplectic group      70
Minimal series (of Virasoro algebra)      245
Modular group      67
Multiplicity (of imaginary root)      12
Multiplicity (of weight)      32
Neveu - Schwarz fermion      221
Non-degenerate invariant bilinear form on principal $A_{1}^{(1)}$       345
Non-degenerate principal admissible weight      113
Non-linear Schr $\ddot{o}$ dinger equation      414 427
Normal product      177
Normalized branching function      269
Normalized branching function (of tensor product)      275
Normalized character (of integrable $\mathfrak{g}$ -module)      62
Normalized character (of principal admissible representation)      95 320
Normalized character (of Virasoro module)      246
Normalized character (of W-algebra)      320
Normally ordered product      177 330
Normally ordered product of -nurnbers of fields      200
Odd delta function $\delta_{odd}(z - w)$       332
One-soliton solution      413
Operator product      184
Orthogonal decomposition      410
Orthogonality relation (of irreducible characters)      160
Parity      177 178
Partition number      37 215
Positive real coroot      13
Primitive central element      9
Primitive imaginary root      9
Primitive vector      274
Principal admissible number      83
Principal admissible subset of coroots      79
Principal admissible weight      79
Principal admissible weight of level and of type $\Delta^{\bigvee}_{(u)+}$       88
Principal affinization      371 372
Principal Cartan subalgebra      366
Principal realization of $A_{1}^{(1)}$       347
Principal specialization      42
Principally specialized character      42
Ramond fermion      225
Real coroot      13
Real root      12
Representation matrix      155
Residue of principal admissible character      113 120 320
Scalar field      197
Schr $\ddot{o}$ dinger representation      352
Semi-infinite wedge space      288 294
Serre relation      265
Shift transformation      194
Shifted current      374 405
Short root      14
Simple coroot      13
Simply-laced Lie algebra      3
Soliton solution (of KdVequation)      392
Soliton solutions of type ( $N_{1},N_{2}$ )of non-lineax Schr $\ddot{o}$ dinger equation)      417
Special index      15
Specialization      42
Specialized character      42
Standard bilinear form      10 25
Strange formula      30 296
Strange formula (for Lie superalgebra)      215
Strictly positive integral form      17
String function      35
Structure constant      297 356
Super Jacobi identity      179 198
Super skew-symmetry      179 198
Super-bracket      198
Super-commutative field      178 187
Symmetric Lie algebra      3
Symmetrizable Cartan matrix      2
Symplectic boson      230 3
Theta function      73
Tier number      5
Tits cone      14
Translation operator $t_{\alpha}$       11 67
Transposed Cartan matrix      2
Transposed Lie algebra      13
Transposed root      301
Twisted lattice      353
Twisted multiplication      356
Type $\overline{Q}$ (of affine Cartan matrix)      136
Unitarizable (of group representation)      155
Unitarizable Virasoro module      242
Unitary form      155
Vacuum state      225
Vacuum vector      230
Verlinde's formula      128
Vertex operator      237 238 323 357 362 375
Virasoro algebra      240
W-algebra      300
Weight (of highest weight $\mathfrak{g}$ -module)      32
Weight space      32
Weyl - Kac character formula      33
Weyl - Kac denominator identity      33
Weyl co-vector      17
Weyl group      11
Weyl vector      17
Wick theorem      185
Witt algebra      240

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