References978-3-540-69617...140 Invent. math. 101, 717 - 736 (1990) References 33. Elliott, E. B.:...
Transcript of References978-3-540-69617...140 Invent. math. 101, 717 - 736 (1990) References 33. Elliott, E. B.:...
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Index
Actioncontracts 91, 93deformation of 93multiplicity-free 33, 59, 60, 62, 73, 97, 98, 100, 108,
116, 127, 129rational 1, 4
Adjunction argument 33, 50
Bideterminant 77Binary forms 33, 55Bitableau 77-79, 81
Canonical unipotent subgroup 80-83Co-adjoint representation 116Codimension 2 condition 22Complexity 51,60, 106, 107, 115, 120, 122, 123, 131, 132,
142, 144Condition (F) 133-136Condition (FM) 129-131, 133, 136Contraction of action 91, 93Covariant 56, 58
Discrete valuation 23-26, 124, 125Discrete valuation ring 23
Epimorphic subgroup 6-8, 10, 18, 19,51,98, 132-137E(w) 71-76, 79, 88, 96-98, 135, 136
First Main theorem 79Frobenius reciprocity 73
Geometryaffine 62, 65Euclidean 65, 67
Good filtration 80, 90, 103, 105Gordan's lemma 123, 124, 126Grosshans subgroup 21-23, 26-30, 32, 51-53, 60, 61, 63-66, 94,
114, 120, 121, 134, 137
Highest weight vector 15-17, 28, 42, 43, 45, 60, 61, 63, 72-74
Induced module 33, 47, 71
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Index
Knop's theorem 122Kritische Nenner 81
Locally nilpotent derivation 48, 58
Moduleco-extendible 39, 40of covariants 96rational 4rationally injective 37, 39
Nagata counter-example 46, 122Normalization 8
Observable envelope 6Observable hull 6Observable subgroup 5-10, 12-14, 17-22,26,27,29, 30, 32,
33, 39-43, 45, 50-52, 68, 71, 82, 83, 97, 120, 126,128, 130-132, 136, 140, 143, 144
Orbit 4
Partition 76, 77Pole of rational function 26Popov-Pommerening conjecture 27, 83, 121, 137Prime divisor 26
Quotient variety 107, 109
Roberts' counter-example 46-49Root system
closed 18quasi-closed 18
S-variety 98-100, 105, 127-129Semi-invariant 33, 56Simply connected group 15Spherical subgroup 59-66, 69, 73, 76, 103, 105, 106, 126-129, 141Stabilizer subgroup 5,6, 10, 11, 13, 16, 17,23,30,31,42,
64,91,99, 103, 114, 122, 128, 129, 131, 132, 136Standard basis theorem 77, 78Straightening 76,77, 83, 139Subgroup
canonical unipotent, see canonical unipotent subgroupepimorphic, see epimorphic subgroupGrosshans, see Grosshans subgrouphorospherical 98
147
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148 Index
observable, see observable subgroupquasi-parabolic 17,42,43,45spherical, see spherical subgroupstabilizer, see stabilizer subgroup
Tensor identity 35Transfer principle 33, 49Transitivity of induction 35
Valuation 23-26, 124, 125Valuation ring 23Value group 23Variety
complete 28determinantal 103unirational 118-120, 124, 125
Weightdominant 15fundamental 15highest 15
Weitzenbock's theorem 54, 55
Young diagram 76Young tableau 76
Zero of rational function 26
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