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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

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

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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