Grosshans F.D. — Algebraic Homogeneous Spaces and Invariant Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Grosshans F.D. — Algebraic Homogeneous Spaces and Invariant Theory

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Название: Algebraic Homogeneous Spaces and Invariant Theory

Автор: Grosshans F.D.

Аннотация:

The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years. This book is an exposition of several related topics including observable subgroups, induced modules, maximal unipotent subgroups of reductive groups and the method of U-invariants, and the complexity of an action. Much of this material has not appeared previously in book form. The exposition assumes a basic knowledge of algebraic groups and then develops each topic systematically with applications to invariant theory. Exercises are included as well as many examples, some of which are related to geometry and physics.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 148

Добавлена в каталог: 24.09.2006

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Предметный указатель

$E(\omega)$       71—76 79 88 96—98 135 136
Action, contracts      91 93
Action, deformation of      93
Action, multiplicity-free      33 59 60 62 73 97 98 100 108 116 127 129
Action, rational      1 4
Adjunction argument      33 50
Bideterminant      77
Binary forms      33 55
Bitableau      77—79 81
Canonical unipotent subgroup      80—83
Co-adjoint representation      116
Codimension 2 condition      22
complexity      51 60 106 107 115 120 122 123 131 132 142 144
Condition (F)      133—136
Condition (FM)      129—131 133 136
Contraction of action      91 93
Covariant      56 58
Discrete valuation      23—26 124 125
Discrete valuation ring      23
Epimorphic subgroup      6—8 10 18 19 51 98 132—137
First Main Theorem      79
Frobenius reciprocity      73
Geometry, affine      62 65
Geometry, Euclidean      65 67
Good filtration      80 90 103 105
Gordan's lemma      123 124 126
Grosshans 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
Knop's theorem      122
Kritische Nenner      81
Locally nilpotent derivation      48 58
Module, co-extendible      39 40
Module, of covariants      96
Module, Rational      4
Module, rationally injective      37 39
Nagata counter-example      46 122
Normalization      8
Observable envelope      6
Observable hull      6

Observable 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 77
Pole of rational function      26
Popov-Pommerening conjecture      27 83 121 137
Prime divisor      26
Quotient variety      107 109
Roberts' counter-example      46—49
Root system, closed      18
Root system, quasi-closed      18
S-variety      98—100 105 127—129
Semi-invariant      33 56
Simply connected group      15
Spherical subgroup      59—66 69 73 76 103 105 106 126—129 141
Stabilizer subgroup      5 6 10 11 13 16 17 23 30 31 42 64 91 99 103 114 122 128 129 131 132 136
Standard basis theorem      77 78
straightening      76 77 83 139
Subgroup, canonical unipotent      see canonical unipotent subgroup
Subgroup, epimorphic      see epimorphic subgroup
Subgroup, Grosshans      see Grosshans subgroup
Subgroup, horospherical      98
Subgroup, observable      see observable subgroup
Subgroup, quasi-parabolic      17 42 43 45
Subgroup, spherical      see spherical subgroup
Subgroup, stabilizer      see stabilizer subgroup
Tensor identity      35
Transfer principle      33 49
Transitivity of induction      35
Valuation      23—26 124 125
Valuation ring      23
Value group      23
Variety, complete      28
Variety, determinantal      103
Variety, unirational      118—120 124 125
Weight, dominant      15
Weight, fundamental      15
Weight, highest      15
Weitzenboeck's Theorem      54 55
Young diagram      76
Young tableau      76
Zero of rational function      26

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