304 INDEX
Hilbert scheme, 104
Hochschild-Serre spectral sequence (HSSS),
88, 198
Hodge bundle, 9
Hodge bundles, 35
Hodge decomposition, 31
Hodge domain, 65
Hodge filtration, 31, 246
Hodge flag, 41
Hodge flags, 73
Hodge metric, 11
Hodge numbers, 34
Hodge representation, 51
Hodge structure of weight n, 31
Hodge structure of weight one, 8
Hodge tensors, 34
Hodge’s theorem, 32
Hodge-Riemann bilinear relations, 8, 33
holomorphic automorphic form of weight n,
17
holomorphic discrete series, 170
homogeneous complex manifold, 8
incidence variety I, 95, 149
infinitesimal character, 72
infinitesimal period relation (IPR), 44
infinitesimal variation of Hodge structure
(IVHS), 46
isogeny, 15
Iwasawa decomposition, 130
K-type, 83, 85, 87
Kostant class, 92, 225
Kostant form, 162
L-graded decomposition, 227
L2-cohomology
group, 83
Lagangian Grassmannian GrL(h,
Ck),
35
Lagrange flag, 43
Lagrange line, 43, 44
Lagrange quadrilateral, 151
length l(w) of an element w W , 228
Levi form (intrinsic), 142
Levi form (of an exhaustion function), 96
limiting mixed Hodge structure (LMHS),
248
limits of discrete series (LDS), 69
limits of discrete series for SL2(R), 14
local cohomology, 117
log analytic variety with slits, 273
logarithmic growth, 18
Matsuki duality, 14, 25, 111
Matsuki orbit triple, 124
Maurer-Cartan equation, 75, 174
Maurer-Cartan matrix, 76
mirror quintic variety, 42
mixed Hodge structure, 245
mixed Hodge structure split over R, 246
modular form, 18
monodromy group, 45
moving frame, 173
Mumford-Tate group, 36
Mumford-Tate group of a variation of
Hodge structure, 45
neat (subgroups), 69
negative line bundle, 12
nilpotent cone, 222
nilpotent orbit, 249
nilpotent orbit theorem, 270
non-classical automorphic cohomology
group, 165
non-classical flag domain, 27, 77
non-compact roots, 62
parabolic subgroup, 35
parabolic Picard modular forms, 236
Penrose transform, 23, 27, 162, 173, 181
period domain, 34
period domain Hodge structures of weight
one, 8
period matrix, 6, 35
periods, 6
Picard modular forms, 173, 293
Plancherel formula, 69
polarized Hodge structure, 33
polarized Hodge structure of weight one, 8
positive line bundle, 12
positive root, 19
primitive decomposition, 248
primitive space, 248
projective frame, 149
property W, 194
pseudo-concavity, 241
q(μ), 77
qc(μ + ρ), 91
quartets, 122
rank of G, 52
rationally connected complex manifold, 237
real form (of a complex Lie group, 14
reductive subgroup, 75
reference flag, 167
regular weight, 23, 69
relative differential, 153
restricted root system, 105, 129
restricted roots, 121
restriction of scalars, 54
root lattice, 19, 53
root spaces, 55
root vector, 19
root vectors, 55
(σ, θ)-stable, 121
σ-nilpotent orbit, 272
Schubert cell, 228
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