Thomas Ch.B. — Representations of Finite and Lie Groups :: Электронная библиотека попечительского совета мехмата МГУ

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Thomas Ch.B. — Representations of Finite and Lie Groups

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Название: Representations of Finite and Lie Groups

Автор: Thomas Ch.B.

Аннотация:

This book provides an introduction to representations of both finite and compact groups. The proofs of the basic results are given for the finite case, but are so phrased as to hold without change for compact topological groups with an invariant integral replacing the sum over the group elements as an averaging tool. Among the topics covered are the relation between representations and characters, the construction of irreducible representations, induced representations and Frobenius reciprocity. Special emphasis is given to exterior powers, with the symmetric group Sn as an illustrative example. The book concludes with a chapter comparing the representations of the finite group SL2(p) and the non-compact Lie group SL2(?).

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2004

Количество страниц: 156

Добавлена в каталог: 17.06.2008

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Предметный указатель

$\lambda$ -structure      55
1-parameter subgroups      81
Abelian group      15 26
Adjoint representation      79 86
Algebraic integer      27
Alternating product      52
Alternating square      14
Brauer character      116
Brauer theorem      95
Burnside's theorem      9
Casimir operator      87
CHARACTER      13
Character table      19—21 23 93 124
Class function      13 18
Clebsch — Gordan formula      71
Complementary series      97
Complexification      84
Differential manifold      75
Discrete series      92 97
Double centraliser condition      8
Double coset formula      45 131
Exponential map      82
Frobenius reciprocity      38
Group ring      3
Groups, , cyclic      1
Groups, $D_{2m}$ , dihedral      10 39 44
Groups, $PSL_2(\mathbb{F}_7)$       23 126
Groups, $P_{\pm}$ , order equals       42 44
Groups, $Q_{4t}$ , quaternion      44
Groups, , characteristic 0 representations      89 92 95 123
Groups, $SL_2(\mathbb{F}_p)$ , characteristic p representations      57
Groups, $SL_2(\mathbb{R})$ , special linear      1 91
Groups, , special unitary      2 43 64 84 86
Groups, , symmetric      44 124
Groups, , symmetric      127
Groups, , unitary      63 81 104 105
Groups, I, icosahedral       21
Groups, O, octahedral       20
Groups, T*, binary tetrahedral $(SL_2(\mthbb{F}_3))$       43
Groups, T, tetrahedral       20
Haar integral et seq.      101

Indecomposable      5
Induced representation, $SL_2(\mathbb{R})$       97
Induced representation, compact      67
Induced representation, finite      35
Irreducible      1
Isotypic      26 67
Jacobson radical      119
Lie algebra      78
Lie algebra, , (representations)      84
Lie group      75
Mackey's criterion      38
Maschke's Theorem      5
Metacyclic group      42
Method of little groups (Mackey — Wigner)      132
Minimal condition      107 109
Mock discrete series      97
Modular representation      115
Orthogonality relations      15
p-regular (p'-element)      116
Principal series      91 97
Product representation $(G_1 \times G_2)$       30
Radical      109
Radical (nilradical)      119
Real representation      31 33
Real representation, Frobenius — Schur Theorem      34
Regular representation      17
Representation      1
Representation ring R(G)      55
Representations of       57
Schur's lemma      5
Semisimple module/ring      4 112
Simple ring      6 108 114
Symmetric group , exterior powers      56
Symmetric group , permutation representation      20
Symmetric product      52
Symmetric square      14
Tangent bundle/vector      75
Tensor product, (advanced)      47
Tensor product, (utility)      12
Topological group      1 63
Wedderburn's Theorem      9
Young diagram      13

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