Simon B. — Representations of Finite and Compact Groups :: Электронная библиотека попечительского совета мехмата МГУ

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Simon B. — Representations of Finite and Compact Groups

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Название: Representations of Finite and Compact Groups

Автор: Simon B.

Аннотация:

A textbook for an upper-level course, more elementary than most by assuming only a prior exposure to the notions of quotient group and the isomorphism theorems. Also approaches representation theory from the perspective of analysis rather than algebra or geometry, as is usually the case. Covers the representation of finite groups of rotations, permutations groups, and classical compact Lie groups.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 266

Добавлена в каталог: 13.01.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$A_{2}$       183
$A_{4}$       63
$A_{5}$       88
$A_{l}$       187
$B_{2}$       183
$B_{l}$       187
$C\mathbb{L}(n)$       68
$C\mathbb{L}_{+}(n)$       73
$C_{l}$       187
$C_{n}$       13
$D^{(\alpha)}_{ij}$       25
$D_{2n}$       13
$D_{l}$       187
$E_{6}$       187
$E_{7}$       187
$E_{8}$       187
$f(\mathcal{F})$       97 98 107
$F_{4}$       187
$GL(n,\mathbb{R})$       135
$G_{2}$       183 187
$L^{p}(G,d\mu)$       135
$sl(2,\mathbb{C})$       174
$S_{3}$       62
$S_{4}$       83
$S_{5}$       86
$S_{m}$       250
$S_{n}$       95 109 110 253
$T \multimapinv T'$       102
$u_{\alpha}$       190
$\mathcal{I}$       210 228 230 231 232
$\mathcal{K}$       208
$\mathcal{R}$       210 228 230 231 232
$\mathcal{T}$       208
$\mathcal{Y}$       210
$\mathcal{Z}$       206
$\pi_{1}(G,e)$       147
$\pi_{n}(X,x_{0})$       146
Abelian group      1 65
Abelization of G      42
Act dually      249
action      3
Ad(x)      130
Adjoint representation      130
Affine group      10
Algebraic integer      43
Algebraic number      43
Alternating space      253
Ambivalent      48
Anti-unitary      30
Automorphism      2
Basis      206
Branching relations      108
Buckyball      16
Burnside's theorem      55
C      13
Cartan      137
Cartan integers      181 197 199 201 203
Cartan subalgebra      166 177 197 199 200 203
Cartan's criterion      171
Center      39
Central projection      56
CHARACTER      35 39 157
Character table      42
Class function      39
Class, ambivalent      48
Classical groups      121 137
Clebsch — Gordan integers      29 119 222
Clifford algebra      68 152
Clifford group      68—75
Column permutations      101
Commutant      248
Commutator subgroup      35 42
Compact groups      121
Compact semisimple Lie group      165
Complex conjugate      30
Complex conjugate representation      30—34
Complex representation      47 72 74 158 242
Conjugacy classes      4 39
Convolution      25 38
Coset      3
Cotangent bundle      123
Cotangent space      123
Covering group      150
cube      13 15 83
CYCLE      9
Degree      21
Differential equations      124
Differential form      123
Dihedral group      8 81
Dimension Theorem      43
Direct product      5 7 59
Direct sum      23
Direct sum of irreps      25
Direct sum of matrix algebras      38
Direct sum representation      24
Disjoint      56
Disjoint cycles      9 95
dodecahedron      13
Dominant forms      211
Dominant weights      211
Double commutant theorem      248
Double cosets      91
Dual frame      117
Dual fundamental system      185
Dual group      34
Dual lattice      210
Dynkin diagram      186 197 199 201 203
EDGE      192
Equivalent      56
Euclidean group      10
Exceptional Lie groups      151
Exterior product      59
Face      192
Fibration      150
Finite abelian group      65
Fourier analysis      57
Fourier transforms      58
Freudenthal      223
Freudenthal's formula      223
Frobenius      77 85 89 109
Frobenius character formula      85 109 247
Frobenius reciprocity theorem      89
Fundamental group      147
Fundamental irreps      228 230 231 232
Fundamental root      184
Fundamental system      184 193 200 203
Fundamental translations      181 197 199 201 203
Fundamental weights      211 228 230 231 232
G-space      2 4
General linear      21
Generator      167
Group      1
Group algebra      25
Group of quaternionic units      31
Group representation      21
Group, abelian      1
Group, topological      2
Groups of order $p^{2}$       19 55
Groups of order pq      19 55
Haar measure      133
Hausdorff — Young inequality      58
Hilbert space      22
Hilbert — Schmidt inner product      38
Hilbert — Schmidt operators      257
Homogeneous space      4
Homomorphism      2
Homotopy group      146
Homotopy product      146
i      13

icosahedron      13 16
Induced representations      83—89
Induction in stages      90
Infinitesimal Cartan — Stiefel diagram      192
Inner automorphism      2 3
Inner product      21
Integral forms      210
Interior product      59
Intertwining map      28
Invariant subspace      24
Irreducible      24
Irreducible character      35 40
Irrep      24
Irreps of an abelian group      28
Isomorphism      2
Isotropy subgroup      4
Jacobi identity      125
Killing form      170 180 197 199 201 203
Klein      11
Kostant      222
Lagrange's theorem      3
Lattice      206
Lattice of weights      210
Left coset      3
Left regular representation      27
Lie algebra      128
Lie bracket      125
Lie group      128
Lie — Trotter formula      131
Lowest form      211
Mackey      91
Mackey irreducibility criterion      91
Manifold      122
Matrix algebras      38
Matrix groups      135
Maximal root      197 199 201 203
Maximal torus      165 196 199 200 203
Maximal weight      217
Minimal central projection      56
Minimal projection      56
Modulus      133
Multiplicity      215
Normal subgroup      2
Normalized      184
octahedron      13
One-dimensional representations      42
Orbit      4
Order      3
Orientable      127
Orientation      127
Oriented      127
orthogonal matrices      10
Orthogonality relations      36 40 157
p-group      16—18
Partitions      96
Pauli $\sigma$ -matrices      73
Permutation group      8
permutations      95
Peter — Weyl theorem      158 257
Platonic groups      13
Poincare' group      10
Point derivation      122
Projection      56
Quaternionic      140
Quaternionic representation      30—34 47 50—54 72 74 158 244 245
Quotient      5
Racah      222
Rank      166
Real representation      32 47 50—54 72 74 158 244 245
Regular element      189
Regular representation      25
Representations of abelian groups      66—67
Representations of tori      173
Representations on quaternion vector spaces      50—54
Representations on real vector spaces      50—54
restrictions      59
Right regular representation      27
root elements      181 197 199 201 204
Root space      178
Root vectors      178 197 199 201 203
Roots      178 197 199 200 203
Rotations      11
Row permutations      101
schur      175
Schur's lemma      27—28 36
Self-conjugate      31
Semidirect product      6 7 77
Semisimple      225
Semisimple Lie group      165
sgn      8
SIGN      8
Sign of permutation      8
Simple root      184
Simply connected      147
Singular element      189
SO(2n+1)      137 200 231 240 245
SO(3)      145
SO(5)      145
SO(N)      11 138 150 152
solvable      225
Sp(1)      144
Sp(2)      145
Sp(N)      140 142 150 203 232 239 245
Spin groups      152
Spin(n)      151 152
Standard tableau      97
Steinberg      222
Strongly dominant forms      211
Strongly dominant weights      211
SU(2)      144 174
SU(N)      137 150 179 182 196 228 237 242 244 250
Subface      192
Subgroup      2
Subgroups of index      2 60—62
Sylow theorems      16
Symmetric group      95 253
Symmetric space      253
Symplectic group      142
t      13
Tangent bundle      123
Tangent space      123
Tensor product      29 253
Tensor product representation      29
Tetrahedral group      82
tetrahedron      13 15
Theorem of Frobenius and Schur      47 256
Topological group      2 121
Torus      165
Transitive      4
Unitarily equivalent      22
Unitary representation      22 26
Universal covering group      149
Vandermonde determinant      238
Vandermonde function      112
Vandermonde polynomial      8
Vector field      123
Weak convergence      257
Wedderburn structure theorem      39
Weights      210 215
Weyl      11 78 158 174 214 221
Weyl chamber      192
Weyl character formula      217 247
Weyl dimension formula      221
Weyl group      192 197 200 201 204 215
Weyl integration formula      213—215
Wigner      77
Young frame      96
Young tableau      97
Z(G)      190

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