Index 405
Fourier transform, 113
modified, 114
non-commutative, 76
free boson operators, 40
Frobenius Integrability Criterion, 24
Frobenius Theorem (on division algebras),
273
Fubini–Study form, 261
functional dimension, 75, 82, 201
functionals, 335
functor, 213
left adjoint, 321
representable, 215
fundamental sequence, 209
fundamental weight, 307
G-bundle, 326
G-equivariant maps, 319
G-manifold, 319, 384
tame, 392
G-orbit, 320
G-space, 319
GK-dimension, 76
g-module, 291
Gelfand-G˚ arding space, 367
generalized exponents, 307
generating function, 257
generator, 257
generic, 155
geometric quantization, 196
graph, 211, 344
Grassmannian, 149
group
unitary dual, 73
groups of Heisenberg type, 94
Hamiltonian field, 257
Hausdorff, 231
Heisenberg group, 33
generalized, 33
Heisenberg Lie algebra, 32
generalized, 32
Hermite functions, 51
Hermite polynomials, 51
Hermitian, 340, 368
Hermitian form, 260
highest weight, 157, 246
Hilbert basis, 338
Hilbert cross-norm, 341
Hilbert dimension, 339
Hilbert space, 337
holomorphic induction, 124, 171
homogeneous
G-bundle, 326
G-set, 321
k-cochain, 217
coordinates, 230
spectrum, 349
homology class, 217
homotopy class, 216
homotopy theory, 216
homotopy type, 216
induction functor, 320
inner automorphism, 276
integrability condition, 253
integrable subbundle, 24
integration, 253
interior point, 207
intermediate, 202
intertwiner, 291, 360
intertwining number, 177, 360
intertwining operator, 176, 291
intertwining operators, 360
invariant
relative, 14
inverse limit, 223
irreducible, 362
isomorphic, 214
isotropic, 258
Jacobi identity, 270
k-boundaries, 217
k-chains, 217
k-cycles, 217
k-irreducible, 363
k-th homology group, 217
ahler form, 261
ahler polarization, 125
ahler potential, 151, 261
Killing form, 310, 316
Kirillov-Kostant form, 163
Kostant partition function, 143
Kronecker Theorem, 285
Lagrangian, 258
Lagrangian fibration, 258
lattice, 307
dual, 140
leaves, 24
left G-set, 318
left H-coset, 322
left action, 319
Leibnitz rule, 241
length, 156, 305, 338
Leray atlas, 232
lie
over, 132
under, 132
Lie algebra, 270
homomorphism, 291
abelian, 297
classical simple, 315
exceptional, 315
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