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

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