INDEX 305

Schubert variations of Hodge structure, 228

semi-basic differential form, 174

Shimura curve, 222, 231, 232

Shimura varieties, 34

Siegel modular form, 178

Siegel’s generalized upper-half-plane Hg, 35

sign reversal of the curvature, 12

simple Hodge structure, 37

simple root, 56

special divisor, 192

splitting of a mixed Hodge structure, 246

standard representation of sl2, 19

strictness of a morphism, 32

structure theorem for a global variation of

Hodge structure, 46

sub-Hodge structure, 32

Tate Hodge structure, 33

Tate twist, 33

theta characteristic, 192

theta function, 24

theta-functions, 294

totally degenerate limit of discrete series

(TDLDS), 70

universal enveloping algebra, 70

universality, 104

variation of Hodge structure (VHS), 44

Vogan diagram, 59

W

(n)

k

, 211

weight decomposition, 31

weight filtration, 246

weight filtration associated to a nilpotent

linear transformation, 248

weight lattice, 19, 52

weight space, 56

weight vector, 19

weights, 19

Weil operator, 32

Weyl group, 19, 55

Williams lemma, 194

Z-connected, 237

Zuckerman module, 117

Zuckerman tensoring, 214