Index
D-modules, 297, 335, 378
A-differential, 101
W-algebra, 249, 320
W-algebra, classical, 289
/37-system, 201
g-oper, 283
0-structure, 122
A-connection, 135
6c-system, 86
n-point functions, 72, 175
adeles, 360
adjoint differential operator, 143
affine connection, 135, 217
affine Grassmannian, 358
affine Kac-Moody algebras, 38, 121, 148,
154, 229, 269, 276, 347, 364
affine structure, 136
annihilation operator, 28, 210
associativity, 48, 180
Atiyah sequence, 148, 379
BGG resolution, 262
Borcherds identity, 56
Borel subalgebra, 190, 282
boson-fermion correspondence, 85
BRST complex, 97, 247, 286, 289
Cartan decomposition, 190, 196, 217, 246
Cartan subalgebra, 190, 246
Casimir tensor, 232, 314
center of a vertex algebra, 95, 273, 319
central charge, 42-44
central extension, 25, 299, 379
central extension, universal, 39
character, 87, 90
charge, 245
Chevalley complex, 165, 380
chiral algebra, 174, 329, 339, 354
chiral correlation functions, 175
chiral de Rham complex, 325, 368
chiral differential operators, 326
chiral Hecke algebra, 372
classical Drinfeld-Sokolov reduction, 285
coinvariants, 153, 168, 297
commutative vertex algebra, 22
configuration space, 225
conformal algebra, 271, 342
conformal blocks, 153, 167
conformal dimension, 16
conformal module, 80
conformal vector, 44
conformal vertex algebra, 44
connection, 117, 148, 276, 377
contraction, 211
coset construction, 95
creation operator, 28, 210
critical level, 214, 216, 320
de Rham cohomology, 156, 240, 343
delta-function, 12, 194, 332, 341, 363
determinant line bundle, 307
disc, 376
disc, abstract, 100
disc, formal, 104, 375
Drinfeld-Sokolov reduction, classical, 285
Drinfeld-Sokolov reduction, quantum, 247
dual Coxeter number, 39
enveloping vertex algebra, 270
external tensor product, 128, 330, 332
factorization algebra, 351
factorization space, 362
fermionic Fock representation, 85
fiber of an O-module, 298
field, 16
flag manifold, 190, 195
flat bundle, 240
flat connection, 117, 377
flat structure, 293, 377
Fock representation, 27, 89, 221, 366
formal coordinate, 100, 111
formal disc, 375
formal distribution, 11
formal Laurent series, 14
formal power series, 11
formal scheme, 375
393
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