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Sepanski R.M. — Compact Lie Groups

Sepanski R.M. — Compact Lie Groups

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Название: Compact Lie Groups

Автор: Sepanski R.M.

Аннотация:

Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Included is the construction of the Spin groups, Schur Orthogonality, the Peter-Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel-Weil Theorem. The necessary Lie algebra theory is also developed in the text with a streamlined approach focusing on linear Lie groups.

Key Features: Provides an approach that minimizes advanced prerequisites, Self-contained and systematic exposition requiring no previous exposure to Lie theory, Advances quickly to the Peter-Weyl Theorem and its corresponding Fourier theory, Streamlined Lie algebra discussion reduces the differential geometry prerequisite and allows a more rapid transition to the classification and construction of representations, Exercises sprinkled throughout. This beginning graduate-level text, aimed primarily at Lie Groups courses and related topics, assumes familiarity with elementary concepts from group theory, analysis, and manifold theory. Students, research mathematicians, and physicists interested in Lie theory will find this text very useful.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 198

Добавлена в каталог: 19.06.2008

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Предметный указатель

$(-1)^{deg}$       31
$(T, S)_{HS}$       72
      118
$B(\dot, \dot)$       124 130
      120
$C(G)_{G-fin}$       61
$C^{\infty}G)$       180
      90
      118
$d\Phi$       19
$D_m(\mathbb{R}^n)$       42
      120
$End(V)_{HS}$       72
      133
      83
      30
      126
      14
      119
$E_{i,j}$       19 118
$e_{\alpha}$       127
$E_{\pi}$       38
      19
$f^V_{u,v}(g)$       47
      71
$F_{\alpha}$       127
$f_{\lambda\otimes x}$       64
$GL(n, \mathbb{F})$       2
$GL(n, \mathbb{H})$       5
$Gr_k(\mathbb{R}^n)$       2
$g\dot v$       27
$G\times_H V$       177
      9
$g^l[(n, \mathbb{F})$       82
$g^l[(n, \mathbb{H})$       85
      9
      4
$G^{reg}$       156
$g_1\oplus g_2$       108
$G_1\times G_2$       51
$g_{\alpha}$       117
$G_{\mathbb{C}}$       178
      28 54
$H_{\alpha}$       127
\mathbb{H})$      11 86
      177
$I_{E_{\pi}}$       67
$ker\mathcal{E}$       131
      47 60
      21 60 81
$L_{\lambda}$       179
$M_{2n,2n}(\mathbb{C})_{\mathbb{H}}$       5
$M_{n,m}(\mathbb{F})$       2
$M_{n,n}(\mathbb{H})$       5
$m_{\pi}$       38
$m_{|x|^2}$       15
$n^{\pm}$       151 178
      94
$Op(\hat{G})$       72
$Pin_n(\mathbb{R})$       16
$P^{\vee}$       130
$R^{\vee}$       130
      21 60
$r_{h_{\alpha}}$       143
$R_{\alpha}$       143
$SL(n, \mathbb{F})$       4
$sl(n,\mathbb{F})$       84
      119
$so(E_n,\mathbb{C})$       119 120
$SO(n, \mathbb{C})$       19
$Sp(n, \mathbb{C})$       6
$Spin_n(\mathbb{C})$       19
$Spin_n(\mathbb{R})$       12 16
$Spin_{p,q}(\mathbb{R})$       19
      2
      34 114
      1
$S^{\pm}$       31
      137
$tr(T_{\pi} \circ g^{-1})$       73
      1
      119
      19
$T_{\lambda}$       63
$t_{\mathbb{C}}(\mathbb{R})$       117
      8
$U^{-1}$       8
$u_{\alpha}$       125
$V \oplus W$       34 114
$V \otimes W$       34 51 114
      29
$V(\lambda)$       153
$V^0_{\pi}$       77
      50
$V_1\bar{ \otimes} V_2$       59
$V_m(\mathbb{R}^n)$       29
$V_n(\mathbb{C}^2)$       28
$V_{G-fin}$       57 77
$V_{p,q}(\mathbb{C}^n)$       46 155
$V_{\alpha}$       116
$V_{\pi}$       58 77
$W(\Delta(g_{\mathbb{C}}))$       143
$W(\Delta(g_{\mathbb{C}})^{\vee})$       143
$X\dot v$       113
      113
$X_{\gamma}$       171
      94
$[v]_{\mathcal{B}}$       35
$\alpha$       16
$\alpha$ -string      129
$\alpha^{\vee}$       125
$\bar{A}$       5
$\bar{V}$       34 114
$\chi(T)$       131
$\chi_V(g)$       49
$\chi_{\lambda}$       153
$\cong$       28
$\Delta$       30 165
$\Delta(g_{\mathbb{C}})^{\vee}$       125
$\Delta(g_{\mathbb{C}},t_{\mathbb{C}})$       117
$\Delta(V,t_{\mathbb{C}})$       116
$\Delta^+(g_{\mathbb{C}})$       139
$\Delta^-(g_{\mathbb{C}})$       139
$\delta_{i,j}$       47
$\Delta_{p,q}$       46
$\epsilon(x)$       14
$\epsilon_i$       118
$\gamma x$       83
$\Gamma(M,\mathcal{V})$       176
$\Gamma_{hol}(G/T, L_{\lambda})$       180
$\hat{f}$       70 76
$\hat{G}$       38
$\int\omega$       20
$\int_G f$       21
$\iota$       159
$\iota(x)$       14
$\lambda_T$       63
$\mathbb{C}^{\times}$       25
$\mathbb{C}_{\lambda}$       179
$\mathbb{F}$       2
$\mathbb{H}$       5
$\mathbb{H}^{\times}$       25
$\mathbb{P}(\mathbb{R}^n)$       2
$\mathbb{R}^{\times}$       25
$\mathcal{A}$       16
$\mathcal{C}^{\pm}_n(\mathbb{R})$       16
$\mathcal{C}_n(\mathbb{C})$       18 31
$\mathcal{C}_n(\mathbb{R})$       13
$\mathcal{C}_{p,q}(\mathbb{R})$       18
$\mathcal{E}$       131

$\mathcal{F}$       73
$\mathcal{H}_m(\mathbb{R}^n)$       30
$\mathcal{H}_{p, q}(\mathbb{C}^n)$       46 155
$\mathcal{I}$       13 73
$\mathcal{S}_n$       137
$\mathcal{T}(\mathbb{R}^n)$       13 34 114
$\omega_g$       21
$\omega_M$       19
$\partial_A$       91
$\partial_q$       42
$\Phi$       15
$\pi$       157
$\pi(f)$       71
$\pi_1(G)$       10
$\prod$       139
$\prod(C)$       140
$\prod(C^{\vee})$       140
$\Psi$       15
$\rho$       140 147
$\theta$       123
$\Theta_{\lambda}$       166
$\tilde{f}$       71
$\tilde{G}$       10
$\tilde{X}$       83
$\tilde{\Phi}$       31
$\tilde{\Phi}^{\pm}$       32
$\tilde{\vartheta}$       5
$\vartheta$       5
$\wedge(\mathbb{R}^n)$       14 34 114
$\wedge^*_n(M)$       19
$\Xi$       156 165
$\xi_f$       163
$\xi_{\lambda}$       131
$\xi_{\lambda}^{\mathbb{C}}$       180
$\zeta(g)$       104 108
$\zeta_g(H)$       94
$\|f\|_{C(G)}$       60
$\|f\|_{L^2(G)}$       60
$\|T\|_{HS}$       72
(it)*      117 125
*      71
<p, q>      42
A      130 178
Abelian      97
action      9
Acts on      27
Ad(g)      90
Adjoint representation      90
Affine Weyl group      172
Alcove      171
algebraic      185
Algebraically integral weights      130
Analytically integral weights      130
Atlas      1
B      178
Borel subalgebra      178
Bruhat decomposition      8
C(G)      47 60
C-positive      140
Campbell — Baker — Hausdorff Series      106
Canonical decomposition      39 59
Cartan, involution      123
Cartan, matrix      132 149
Cartan, subalgebra      98
Center      7
centralizer      94
Change of variables formula      20
CHARACTER      49
Character, group      131
Chart      1
Chevalley’s Lemma      148
Class function      67
Classical compact Lie groups      4
Clebsch — Gordan formula      53 70
Clifford algebra      13
Clifford algebra, conjugation      16
Closed subgroup      3
Commutator subgroup      69 109
Compact operator      56
Completely reducible      37
complex type      53
Complexification      115 178
Conjugate space      34
Connected      8
Convolution      71
coordinates      88
Cotangent space      19
Covering      10
d(t)      156 161
Descends      163
dg      21
Differential      19 88
Dolbeault cohomology      184
Dominant      151
Dual basis      35 47
Dual lattice      131
Dual root lattice      130
Dual space      34
Dual weight lattice      130
Dynkin, diagram      140
Dynkin, Formula      106
e      115 127
End(V)      71
Equivalent      28 54 176
Euler angles      25
exp(X)      83
Exterior algebra      14
Exterior bundle      19
Exterior multiplication      14
f      115 127
Faithful representation      66
Fiber      176
Frechet space      55
Frobenius reciprocity      177
Fundamental group      10
Fundamental weight      140
G      2
G'      69 109
g*      4 5
G-finite vectors      57 77
G-invariant      36 54
G-map      28 54
General linear group      2
Genuine      30
GL(V)      2 54
Grassmannian      2
gv      27
H      115 127
Haar measure      21
Half-spin representation      31
Harmonic polynomials      30
Highest root      147
Highest weight      151
Highest weight, classification      169
Highest weight, vector      151
Hilbert space      55
Hilbert space, direct sum      57
Hilbert space, tensor product      59
Hilbert — Schmidt, inner product      72
Hilbert — Schmidt, norm      72
Holomorphic      180
Hom(V, V')      27 34 54 114
Homogeneous      176
Homomorphism      3 89
Imaginary quaternions      11 86
Imbedded submanifold      3
Immersed submanifold      2
Immersion      2
Indecomposable      140
Induced representation      177

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