Index
a representation that leads to a Hodge
representation, 53
anisotropic maximal torus, 38
anti-dominant Weyl chamber, 71
arithmetic structure (on automorphic
cohomology, 221
automorphic cohomology, 154
basic diagram, 149
Beilinson-Bernstein localization, 117
Blattner parameter, 202
Borel subgroup, 19
Borel-Weil-Bott theorem, 23
Bruhat cell, 181
canonical extension of the Hodge bundle, 18
Cartan decomposition, 53
Cartan involution, 53
Cartan sub-algebra, 19, 55
Cartan subgroup, 35
Cartan-Killing form, 55
Casimir operator, 200
Casselman-Osborne lemma, 194
Cauchy-Reimann subspace (of the tangent
space), 135
Cauchy-Riemann tangent space, 99, 133
Cayley transform, 124, 254
center of the universal enveloping algebra,
70
character, 52
Chern form, 11, 75
Chow’s theorem, 238
classical flag domain, 27, 77
CM field, 48
co-character, 52
co-root vectors, 55
compact dual
ˇ
D of a period domain D, 34
compact dual of the period domain for
Hodge structures of weight one, 8
compact roots, 62
completion of a variation of Hodge
structure, 222
complex multiplication (CM) Hodge
structure, 37, 46
congruence subgroup, 16
conservation law (for orbit codimensions,
128
correspondence diagram, 22
correspondence space, 21
correspondence space W, 95, 148
correspondence spaces, 27
cusp, 17
cusp form, 18
cuspidal automorphic cohomology, 221
cycle space U, 95, 102
cycle spaces, 27
Deligne splitting (of a Hodge structure),
246
differential form, type of, 7
discrete series (DS), 69
discrete series for SL2(R), 14
dominant Weyl chamber, 55
dual pair, 111
enhanced flag variety, 147
exhaustion function , 96
exhaustion function modulo GR, 108
expanding cohomology about Z, 86
fan, 222, 272
flag domain, 14, 72
flag variety, 14, 72
(gC, KC)-module, 71
grading, 53
grading associated to a filtration, 246
grading element, 227
Grauert domain, 107
Grothendieck residue symbol, 120
Gysin map, 33
Harish-Chandra module, 14, 70
Harish-Chandra parameter, 83, 202
Hermitian symmetric domain, 77
Hermitian type (of G), 109
Hermitian vector bundle, 35
highest weight, 56
highest weight vector, 72
303
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