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