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Collingwood D.H., McGovern W.M. — Nilpotent Orbits in Semisimple Lie Algebras
Collingwood D.H., McGovern W.M. — Nilpotent Orbits in Semisimple Lie Algebras



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Название: Nilpotent Orbits in Semisimple Lie Algebras

Авторы: Collingwood D.H., McGovern W.M.

Аннотация:

Through the 1990s, a circle of ideas emerged relating three very different kinds of objects associated to a complex semisimple Lie algebra: nilpotent orbits, representations of a Weyl group, and primitive ideals in an enveloping algebra. The principal aim of this book is to collect together the important results concerning the classification and properties of nilpotent orbits, beginning from the common ground of basic structure theory. The techniques used are elementary and in the toolkit of any graduate student interested in the harmonic analysis of representation theory of Lie groups. The book develops the Dynkin-Konstant and Bala-Carter classifications of complex nilpotent orbits, derives the Lusztig-Spaltenstein theory of induction of nilpotent orbits, discusses basic topological questions, and classifies real nilpotent orbits. The classical algebras are emphasized throughout; here the theory can be simplified by using the combinatorics of partitions and tableaux. The authors conclude with a survey of advanced topics related to the above circle of ideas. This book is the product of a two-quarter course taught at the University of Washington.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 186

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adjoint group      8
Adjoint orbit      9
Adjoint orbit, as a homogeneous space      10
Adjoint orbit, as a sympletic manifold      17
Adjoint representation      1
Annihilator in polynomial ring      3
Annihilator in the enveloping algebra      171
Associated variety      171
Automorphism group      7
Bala - Carter classification      124
Bala - Carter Theory      119
Borel subalgebra      32
Cartan decomposition      136
Cartan involution      136
Cartan subalgebra      19 120
Cayley triples      145
centralizer      10
Centralizer, classical component groups      88
Centralizer, component group      87
Centralizer, component groups      88
Centralizer, of a nilpotent element      49
Centralizer, of a semisimple element      20
Characteristic cycle      175
Classical algebras      11
Classical groups      10
Classification, Bala - Carter      124
Classification, classical cases      69
Classification, classical real nilpotent orbits      139
Classification, exceptional nilpotent orbits      127
Classification, nilpotent orbits      37
Classification, primitive ideals      173
Classification, real forms      135
Classification, semisimple orbits      25
Classification, strategy      32
Coadjoint orbit      11
Collapse operation      99
Conjugacy class      9
Conjugacy theorem, Cayley triples      145
Conjugacy theorem, Kostant      36 42
Conjugacy theorem, Mal'cev      36 43
Conjugacy theorem, minimal Levi subalgebras      120
Conjugacy theorem, normal triples      145
Conjugacy theorem, Rao      146
Conjugacy theorem, real standard triples      138
Diagonalizable operator      1
Distinguished nilpotent elements      121
Distinguished nilpotent orbits      121
Distinguished nilpotent orbits, classical cases      126
Distinguished nilpotent orbits, even      122
Distinguished parabolic subalgebra      123
Distinguished parabolic subalgebra, as Jacobson - Morozov      124
Distinguished semisimple orbits      29
Dixmier algebras      177
Dominant      45
Duflo's Theorem      172
Even nilpotent orbit      53 85 122
Even nilpotent orbit, Richardson      110
Exceptional cases      127
Exceptional cases, dimension      127
Exceptional cases, fundamental group      127
Exceptional cases, real      150
Exceptional cases, special      127
Exceptional cases, weighted Dynkin diagrams      127
Expansion operation      101
Exponents of a semisimple group      64
Finiteness Theorem, complex nilpotent orbits      46
Finiteness Theorem, real nilpotent orbits      150
Fundamental group      87
Fundamental group, any orbit      93
Fundamental group, equivariant      88
Fundamental group, exceptional cases      91 92
Generalized eigenspace decomposition      3
generic elements      21
Goldie rank polynomial      173
Harish - Chandra module      174
Hasse diagram      93
Hasse diagram, classical cases      93
Hasse diagram, duality map      102
Hasse diagram, exceptional cases      103
Hasse diagram, order reversing map      100
Hermitian form      140
Induced nilpotent orbit      106
Induced nilpotent orbit, $\mathfrak{sl}_{n}$      112
Induced nilpotent orbit, diagram in classical cases      116
Induced nilpotent orbit, dimension      108
Induced nilpotent orbit, independence of $\mathfrak{p}$      107
Induced nilpotent orbit, induction in stages      108
Induced nilpotent orbit, meeting a Levi subalgebra      127
Induced nilpotent orbit, partition in $\mathfrak{sl}_{n}$      113
Induced nilpotent orbit, partition in classical cases      116
Induced nilpotent orbit, weighted Dynkin diagram      109
Irreducibility theorem      172
Isometry group      70
Isotropic submanifold      16
Jacobson - Morozov Theorem      36-37 137
Jordan block      31
Jordan decomposition theorem      2
Killing form      11
Left cell representation      174
Metaplectic representation      109
Minimal Levi subalgebras      120
Minimal nilpotent orbit      55 61
Minimal nilpotent orbit, partition      85
Minimal nilpotent orbit, rigid      109
Minimal nilpotent orbit, when even      85
Neutral element      33
Nilnegative element      33
Nilpositive element      33
Nilpotent cone      68
Nilpotent cone, as an irreducible variety      68
Nilpotent distinguished elements      121
Nilpotent element      2
Nilpotent in $\mathfrak{g}^{*}$      13
Nilpotent operator      1
Nilpotent orbit      9
Nilpotent orbits in $\mathfrak{sl}_{n}$      32
Nilpotent orbits, classical fundamental groups      91
Nilpotent orbits, dimension      90
Nilpotent orbits, dimension in $\mathfrak{sl}_{n}$      112
Nilpotent orbits, distinguished      121
Nilpotent orbits, exceptional cases      127
Nilpotent orbits, exceptional fundamental groups      92
Nilpotent orbits, exceptional real orbits      150
Nilpotent orbits, fundamental group      87
Nilpotent orbits, Hasse diagram      55
Nilpotent orbits, in      70
Nilpotent orbits, in $\mathfrak{sl}_{n}$      69
Nilpotent orbits, in $\mathfrak{sl}_{n}$($\mathbb{R}$)      140
Nilpotent orbits, in $\mathfrak{so}_{2n+1}$      69
Nilpotent orbits, in $\mathfrak{so}_{2n}$      141
Nilpotent orbits, in $\mathfrak{so}_{n}^{*}2n$      141
Nilpotent orbits, in $\mathfrak{sp}_{n}$      70
Nilpotent orbits, in $\mathfrak{su}_{n}^{*}2n$      140
Nilpotent orbits, in $\mathfrak{su}_{p,q}$      140
Nilpotent orbits, induced      106
Nilpotent orbits, ordering      95
Nilpotent orbits, partial ordering      55
Nilpotent orbits, Richardson      106
Nilpotent orbits, rigid      109
Nilpotent orbits, special      100
Nilpotent orbits, topology      87
Nilradical      32
Normal triple      145
Orbit, adjoint      9
Orbit, nilpotent      9
Orbit, semisimple      9
Parabolic subalgebra      51
Parabolic subalgebra, distinguished      123
Parabolic subalgebra, Jacobson - Morozov      52
Parabolic subalgebra, partition      111
Partition      30
Partition, collapse      99
Partition, expansion      101
Partition, for minimal orbit      85
Partition, for principal orbit      85
Partition, for subregular orbit      85
Partition, ordering      93
Partition, parabolic subalgebra      111
Partition, special      100
Partition, transpose      65 98
Partition, very even      70
Poincar$\acute{e}$ - Birkhoff - Witt      171
Primitive ideal      171
Principal nilpotent orbit      46 55-56
Principal nilpotent orbit, partition      85
Principal nilpotent orbit, when even      85
Real forms      135
Real nilpotent orbits      139
Real nilpotent orbits, classical cases      139
Real nilpotent orbits, in $\mathfrak{sl}_{n}$      140
Real nilpotent orbits, in $\mathfrak{so}^{*}2n$      141
Real nilpotent orbits, in $\mathfrak{so}_{p,q}$      141
Real nilpotent orbits, in $\mathfrak{su}^{*}2n$      140
Real nilpotent orbits, in $\mathfrak{su}_{p,q}$      140
Real simple Lie algebras      135
Reductive      4
Regular semisimple      21
Regular semisimple element      21
Regular subalgebra      119
Representations of $\mathfrak{sl}_{n}$      34
Richardson orbit      106
Richardson orbit, $\mathfrak{sl}_{n}$      112
Richardson orbit, even      110
Richardson orbit, subregular orbit      110
Rigid nilpotent orbit      109
Rigid nilpotent orbit, $\mathfrak{sl}_{n}$      112
Rigid nilpotent orbit, classical cases      116-117
Root space decomposition      20
Sekiguchi's bijection      147
Semisimple element      2
Semisimple in $\mathfrak{g}^{*}$      13
Semisimple operator      1
Semisimple orbit      9
Semisimple regular      21
Sign representation      166
Signature of a form      140
Signed Young diagram      140
Skew - Hermitian form      140
Spaltenstein map      100
Special nilpotent orbit      100
Special nilpotent orbit, duality      102
Special partition      100
Spectral decomposition      3
Springer correspondence      165 169
Springer correspondence, type $A_{n}$      166
Springer correspondence, type $D_{n}$      168
Springer correspondence, types $B_{n}$ and $C_{n}$      166
Standard triple      33
Standard triple, neutral element      33
Standard triple, nilnegative element      33
Standard triple, nilpositive element      33
Standard triples in $\mathfrak{sl}_{n}$      35 76
Standard triples in $\mathfrak{so}_{2n+1}$      78
Standard triples in $\mathfrak{so}_{2n}$      79
Standard triples in $\mathfrak{sp}_{2n}$      77
Standard triples, Cayley      145
Standard triples, normal      145
Subregular nilpotent orbit      55 59
Subregular nilpotent orbit, partition      85
Subregular nilpotent orbit, Richardson      110
Subregular nilpotent orbit, when even      85
symbols      166
Symmetric form      140
Symplectic form      140
Symplectic manifold      16
Symplectic vector space      15
Toral subalgebra      120
Transpose partition      65 98
Very even partition      70
Weighted Dynkin diagram      29 37 46
Weighted Dynkin diagram, exceptional cases      127
Weighted Dynkin diagram, exceptional real orbits      150
Weighted Dynkin diagram, in $\mathfrak{sl}_{n}$      47
Weighted Dynkin diagram, in $\mathfrak{so}_{2n+1}$      82
Weighted Dynkin diagram, in $\mathfrak{so}_{2n}$      83
Weighted Dynkin diagram, in $\mathfrak{sp}_{n}$      81
Weighted Dynkin diagram, induced orbit      109
Weighted Dynkin diagram, real cases      148
Weyl group      25
Weyl group representation symbols      166
Weyl group representations, $\hat{S}_{n}$      166
Weyl group representations, left cell      174
Weyl group representations, type $D_{n}$      168
Weyl group representations, types $B_{n}$ and $C_{n}$      166
Young diagram      65
Young diagram, signature      140
Young diagram, signed      140
Young tableau      166
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