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| Cahn R.N. — Semi-Simple Lie Algebras and Their Representations |
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| Предметный указатель |
 53 70
 62 70
 56 70
 60 70
 71
 71
 71
 71
 70
, Cartan matrix 48
, representations 112 113
Abelian subalgebra 14 22
AD 12
Adjoint representation 12 31.
Algebra, semi-simple 22
Algebra, simple 22
Allowable set 64
Alternating function 104
Basic representation 81
Bilinear forms 29 135
Bilinear forms, anti-symmetric 135—139
Bilinear forms, invariance 28 29
Bilinear forms, Killing 17
Bilinear forms, symmetric 135—139
Boerner, H. 83
Branching rules 144
Campbell — Baker — Hausdorff theorem 2
Carruthers, P. 16
Cartan matrix 45
Cartan matrix for 54
Cartan matrix for 62
Cartan matrix for 57
Cartan matrix for  60
Cartan subalgebra 14 19 25
Casimir operator 6 84 87 89
Chain of roots 117
Character of a representation 103
Classical Lie algebras 52
Commutation relations 11 30
Commutator 3
Conjugacy classes 124
Dimension of a representation 111 112
Dimension of a representation for SU(n) 114
Dirac bra-ket notation 15
Dual space 15
Dynkin i 49—51 63 83 98 127 143 153
Dynkin, coefficients 74
Dynkin, diagram 49
Dynkin, diagram for 54
Dynkin, diagram for 62
Dynkin, diagram for 57
Dynkin, diagram for 60
Dynkin, extended diagrams 148
Dynkin, Method of Parts 111
Dynkin, Second Highest Rep. Theorem 117
Exceptional Lie algebras 64
Exceptional Lie algebras, Dynkin digrams for 70 71
Extended Dynkin diagram 131
Extended Weight Scheme 148
Freudenthal’s recursion formula 91—94
Functional 15
Fundamental representation 80
Gasiorowicz, S. 16
Gell — Mann matrices 10 16
Georgi, H. ii 83
Golubitsky, M. 134 143
Gottfried, K. 8
Height of a representation 139
Hermitian matrix 7
Ideal 22
Index of a representation 90
Index of an embedding 140
Index of product representations 126
Invariance of Killing form 28
Invariant function 103
Invariant subspace 6
Irreducible representation 6
Jacobi identity 3
Jacobson 8 24 30 38 42 48 63 64 72 83 98 101 102 114
Killing form 17
Killing form, invariance of 28
Killing form, non-degeneracy of 23
Killing form, relation to semi-simplicity 23
Kostant’s formula 116
Level 46
Lie algebra 3
Lie product 3
Maximal subalgebra 130 134 142
Mc Kay, W. B. 143 146 153
Method of Parts 121
Miller, W. 63
O(7) 81
| Operators, Casimir 6 84 87 89
Operators, lowering 4 34
Operators, raising 4 34
Orthogonal group 57
Patera, J. 143 146 153
Pauli matrices 8 10
Positive root 43
Positive root, algorithm for finding 46—47
Product representation 7 79 116
R-subalgebra 130
Rank 45
Reducible representation 6
Regular element 26
Regular subalgebra 129
Representation 4 32
Representation, adjoint 32 39
Representation, basic 81
Representation, character of 103
Representation, dimension of 111
Representation, fundamental 80
Representation, index of 90
Representation, irreducible 6
Representation, product 7 79 116
Representation, product, antisymmetric 80
Representation, product, symmetric 80
Representation, reducible 6
Representation, spinorial 124
Root vectors 15 26
Roots 15
Roots,  set of 29
Roots, positive 43
Roots, simple 43
Roots, simple,  set of 44
Rotation group 1
Rothschild, B. 134 143
S-subalgebra 130
Scalar product on  20
Scalar product on for SU(3) 21
Scalar product on in root space 42
Schensted, I. 83
Second highest representation 117
Semi-simple algebra 22
Simple algebra 22
Simple root 43
Slansky, R. 127 143
SO(10), Dynkin coefficients 77
SO(10), representations 113
SO(2n), Cartan matrix 60
SO(2n), Killing form 59
SO(2n+l), Cartan matrix 62
SO(2n+l), Killing form 61
SO(7) 81
Sp(2n) 55
Sp(2n), Cartan matrix 57
Spinorial representation 124
String of weights 34 40
SU(2) 1 7
SU(2), Casimir operator for 88
SU(3) 9
SU(3), 27 dimensional representation 95 99
SU(3), adjoint representation 12
SU(3), Cartan matrix 46
SU(3), Dynkin coefficients 75
SU(3), Freudenthal formula applied to 95
SU(3), Killing form 18
SU(3), root vectors 21
SU(3), weight vectors 33
SU(3), Weyl group 99
SU(N) 53 114
Subalgebra 22 128
Subalgebra, Abelian 14 22
Subalgebra, Cartan 14 25
Subalgebra, maximal 130
Subalgebra, proper 6
Subalgebra, R- 130
Subalgebra, regular 129
Subalgebra, S- 130
Triality 124
U(3) 22
Unitary matrix 7
Vector space 3
Vector space, weight 33 73
Vector, root 15 26
Weight 33 73
Weight space 37 76
Weight vector 33
Weyl, character formula 111
Weyl, dimension formula 111 112
Weyl, group 36 98
Weyl, reflection 36 99
Young tableaux 83 114 116 121
Young tableaux, correspondence with Dynkin diagram 114
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