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