INDE X A2, 183 A4, 63 A5, 88 At, 187 abelian group, 1, 65 abelization of G, 42 act dually, 249 action, 3 Ad(», 130 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 B 2 , 183 B£i 187 basis, 206 branching relations, 108 Buckyball, 16 Burnside's theorem, 55 C, 13 Gn, 13 C/, 187 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, ambivalent, 48 class function, 39 classical groups, 121, 137 Clebsch-Gordan integers, 29, 119, 222 Clifford algebra, 68, 152 Clifford group, 68-75 CL(n), 68 CL+(n), 73 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 D2n, 13 /#(,), 25 De, 187 degree, 21 differential equations, 124 differential form, 123 dihedral group, 8, 81 dimension theorem, 43 263
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