Symmetry and spaces : in honor of Gerry Schwarz / edited by H.E.A. Campbell ... [and others].

Format:

Book

Contributor:

Campbell, H. E. A. Eddy (Harold Edward Alexander Eddy), 1954-

Schwart, Gerry.

Series:

Progress in mathematics, 0743-1643 ; 278.

Progress in mathematics, 0743-1643 ; 278

Language:

English

Subjects (All):

Characteristic classes.

Invariants.

Geometry, Algebraic.

Genre:

Festschriften.

Physical Description:

xx, 207 pages : illustrations ; 24 cm.

Place of Publication:

Boston, Mass : Birkhäuser ; London : [Springer [distributor], 2010.

Summary:

A group of Gerry schwarz's colleagues and collaborators gathered at the fields Institute in Toronto for a mathematical festschrift in honor of his 60th birthday. This volume is an outgrowth of that event, covering the wide range of mathematics to ehich Gerry Schwarz has either made fundamental contributions or stimulated others to pursue. The articles are a sampling of modern day algebraic geometry with associated group actions from its leading experts, with a particular focus on characteristic 0 and modular invariant theory.

Contents:

Some Basic Results on Actions of Nonaffine Algebraic Groups / Michel Brion 1

1 Introduction 1

2 Proof of Theorem 1.1 5

3 Proof of Theorem 1.2 9

4 Proof of Theorem 1.3 11

5 Proof of Theorem 1.4 13

6 Examples 14

References 20

On Chevalley-Shephard-Todd's Theorem in Positive Characteristic / Abraham Broer 21

1 The direct summand property and point-stabilizers 22

2 Main result and tools for the proof 25

2.1 Tools 26

3 Details 28

3.1 Families 29

3.2 Exceptional cases 33

References 34

Families of Affine Fibrations / Daniel Daigle, Gene Freudenburg 35

1 Introduction 35

2 Preliminaries 36

2.1 Notation and definitions 36

2.2 Some known results on affine nbrations 37

2.3 Locally nilpotent derivations 38

3 A criterion for affine fibrations 39

4 Dimension four 41

5 A remark on stable variables 42

References 43

On the Depth of Modular Invariant Rings for the Groups CpxCp / Jonathan Elmer, Peter Fleischmann 45

1 Introduction 45

2 Flatness and strong flatness 47

3 A sufficient condition for strong flatness 49

4 Groups of the form CpxCp 52

5 Decomposable representations 55

References 60

Kh̃lerian Reduction in Steps / Daniel Greb, Peter Heinzner 63

1 Introduction 63

1.1 Reductive group actions on Kahler spaces 66

1.2 Stratifying holomorphic G-spaces 67

1.3 Kh̃lerian reduction 68

2 Reduction in steps 71

2.1 Analytic reduction in steps 72

2.2 Kh̃lerian reduction in steps 75

2.3 Stratifications in steps 77

3 Projectivity and Kh̃lerian reduction 78

References 81

On Orbit Decompositions for Symmetric k-Varieties / A.G. Helminck 83

1 Introduction 83

2 Preliminaries about symmetric k-varieties 85

2.1 Notations 85

2.2 Classification of symmetric k-varieties 87

2.3 k-Anisotropic symmetric subgroups 88

3 Orbits of parabolic subgroups acting on symmetric varieties 90

3.1 k Algebraically closed and P = B aBorel subgroup 91

3.2 k Algebraically closed and P a parabolic subgroup 92

3.3 Parabolic subgroups with cr-stable Levi subgroups 93

3.4 Some examples 94

3.5 k=k and P a minimal parabolic k-subgroup 96

4 Conjugacy classes of -̤stable tori 98

4.1 W-Action on V A and V K 98

4.2 Action of the Weyl group on twisted involutions 100

4.3 Conjugacy classes of σ-stable maximal A-split tori 101

4.4 tfrConjugacy classes in Aσk for G = SL(2,k) 104

5 Bruhat order and twisted involution posets 105

5.1 Combinatorics of twisted involutions 107

5.2 Lifting σ' to an involution of G 110

5.3 a-Stable parabolic subgroups 112

5.4 Relation between σ and σ' 113

5.5 W-Actionon Jσ 114

5.6 Orbit closures 114

5.7 Bruhat order on V a and V K 116

5.8 Combinatorial Bruhat order on V a 117

5.9 Admissible sequences in V 118

5.10 Bruhat order on J and Jσ' 119

5.11 Combinatorics of the Richardson-Springer involution poset 122

6 Other orbit decompositions 123

6.1 Orbits of symmetric subgroups 123

6.2 Orbits of parahoric subgroups 124

References 125

Root Systems for Levi Factors and Borel-de Siebenthal Theory / Bertram Kostant 129

0 Introduction 129

0.1 129

1 Levi Factor Foot System 131

1.1 131

1.2 132

1.3 135

2 Properties of the t-root System 136

2.1 136

2.2 138

2.3 140

2.4 141

3 Borel-de Siebenthal Theory, Special Elements, and the Lie Subalgebras they Define 144

3.1 144

3.2 146

3.3 147

3.4 148

4 Example 150

4.1 150

References 152

Polarizations and Nullcone of Representations of Reductive Groups / Hanspeter Kraft, Nolan R. Wallach 153

1 Linear subspaces of the nullcone 153

2 Some examples 155

3 General polarizations 158

4 Nullcone of several copies of binary forms 159

5 Generators and system of parameters for the invariants of 3-qubits 162

References 166

Decomposing Symmetric Powers of Certain Modular Representations of Cyclic Groups / R. James Shank, David L. Wehlau 169

1 Introduction 169

2 Preliminaries 173

3 Computing F[VP+)z/p2 176

4 The Noether number of VP+1 183

5 Decomposing F[Vp+1] 187

6 Generating functions 191

References 195

Differential Operators on Grassmann Varieties / Will Traves 197

1 A fundamental theorem 199

2 The Hilbert series of GrD(R) G and GrD(R G ) 203

References 206.

ISBN:

9780817648749

OCLC:

436264805