Index 407
operator calculus, 347
opposite Borel subalgebras, 153
orbit
integral, 157
orientable, 233
orientation, 233
orthogonal, 338
orthonormal, 338
orthoprojector, 340, 386
P -admissible, 24
p-adic integers, 210
p-adic norm, 210
p-adic numbers, 210
parabolic, 153
parallelogram identity, 337
partition of unity, 255
Plancherel measure, 76, 370
Planck constant, 39
normalized, 39
Poincar´ e polynomial, 157
Poisson bracket, 258, 263
polarization
algebraic admissible, 27
complex, 25
complex algebraic, 27
real, 24
real algebraic, 27
polyvector field, 242
Pontryagin dual, 65
positively related charts, 233
principal series, 384
proper, 297
proper map, 236
pseudo-K¨ ahler form, 261
Pukanszky condition, 111
Pythagorean Theorem, 338
quantization rules, 196
quaternions, 273
real form, 316
reduced decomposition, 306
reflexive, 336
regular, 155, 300
relative cohomology, 220
relative trace, 122
representation
absolutely irreducible, 246
adjoint, 276
algebraically irreducible, 363
induced, 371
linear, 291
metaplectic, 184
topologically irreducible, 363
unitary, 357
unitary induced, 382
weights of, 246
representing function, 330
restriction functor, 320
restriction-induction principle, 64
rigged coadjoint orbits, 123
rigged momentum, 123
right G-set, 319
right action, 319
rigid, 292
root, 298
decomposable, 300
negative, 314
positive, 314
simple, 300
root lattice, 307
root system, 298
root vector, 314
scalar product, 337
of quaternions, 273
Schouten bracket, 249
Schur functor, 186
second amendment to Rule 2, 125
second index, 138
section, 372
G-invariant, 327
self-adjoint, 344
semidirect product, 297
separable, 339
separate, 392
sequentially continuous map, 208
Shatten ideal, 185
sign rule, 289
signature, 294
simple spectrum, 346, 349
singular, 300
singular k-cycle
real, integral, 11
skew field, 272
skew product, 239
skew-gradient, 257
small categories, 213
smooth vector, 363
spectral data, 350
spectral function, 348
spectrum
homogeneous, 346
spinor, 20
split real form, 314
stabilizer, 322
Stokes formula, 254
strong integral, 336
subcategories, 212
subexponential, 202
submanifold
Lagrangian, 24
smooth, 228
subordinate, 26
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