Blessenohl D., Schocker M. — Noncommutative Character Theory of the Symmetric Group :: Электронная библиотека попечительского совета мехмата МГУ

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Blessenohl D., Schocker M. — Noncommutative Character Theory of the Symmetric Group

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Название: Noncommutative Character Theory of the Symmetric Group

Авторы: Blessenohl D., Schocker M.

Аннотация:

"This is the first account in book form entirely devoted to the new "noncommutative method". As a modern and comprehensive survey of the classical theory the book contains such fundamental results as the Murnaghan-Nakayama and Littlewood-Richardson rules as well as more recent applications in enumerative combinatorics and in the theory of the free Lie algebra. But it is also an introduction to the vibrant theory of certain combinatorial Hopf algebras such as the Malvenuto-Reutenauer algebra of permutations." The three detailed appendices on group characters, the Solomon descent algebra and the Robinson-Schensted correspondence makes the material self-contained and suitable for undergraduate level. Students and researchers alike will find that noncommutative character theory is a source of inspiration and an illuminating approach to this versatile field of algebraic combinatorics

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 184

Добавлена в каталог: 17.06.2008

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

Предметный указатель

Algebra, centre      128
Algebra, commutative      18
Algebra, connected      5
Algebra, coplactic      see coplactic
Algebra, descent      see descent
Algebra, dual      see dual
Algebra, graded      5 31
Algebra, homomorphism      22 62
Algebra, Hopf      see Hopf
Algebra, Joellenbeck      see Jollenbeck
Algebra, opposite      129
Algebra, semi-simple      2 125 126
Algebra, sub-      18
Bialgebra      20
Bialgebra of class functions      4 25 31
Bialgebra of permutations      9 46 50 51
Bialgebra, dual      21
Bialgebra, homomorphism      22
Bialgebra, self-dual      21
Bialgebra, sub-      20
Bidigare      139
Bilinear form on $\mathcal{C}$       5 30
Bilinear form on $\mathcal{P}$       10 50
Bilinear form, regular      19
Branching rule      89 98
Carpet      151 152
cell      36 see
Centre      see algebra
CHARACTER      2 130 136
Character, cyclic      see cyclic
Character, degree      13 130
Character, descent      see descent
Character, Foulkes      see Foulkes
Character, induced      133
Character, irreducible      2 13 84 106 107 130 137
Character, noncommutative      13
Character, regular      13 86 131
Character, sign      87 102 110
Character, skew      86 91
Character, trivial      29 63 131
Character, Young      see Young
Characteristic      see Frobenius
Class function      2 132
Class function, bialgebra of      see bialgebra
Class function, induced      133
Class, conjugacy      see conjugacy class
Class, coplactic      see coplactic
Class, descent      see descent
Class, number      27 135 137
Class, plactic      see plactic
Coalgebra      18
Coalgebra, cocommutative      18 31
Coalgebra, dual      see dual
Coalgebra, homomorphism      22
Coalgebra, sub-      18
Cocommutative      see coalgebra
column      see frame
Column in $\mathbb{Z} \times \mathbb{Z}$       36
Completely reducible      see module
composition      6
Concatenation      6
Conjugacy class      26 132
conjugate      see partition
Connected      see algebra frame
Content      see word
Convex      53
Convolution product      see product
Coplactic algebra      11 70 75
Coplactic class      12 67 72 76 144 151 152
Coplactic equivalence      67 143
Coplactic neighbour      67 143
Coproduct      4 18
Coproduct on $\mathcal{C}$       29 31
Coproduct on $\mathcal{P}$       46 50
Correspondence      see Robinson
Coupling      see frame
Crochet lemma      148
Cycle, product      3
Cycle, standard      117
Cycle, type      10 26
Cyclic character      117
Degree      see character
Descent algebra      7
Descent character      113
Descent class      93 114
Descent number      93 111
Descent set      7 93 112
Dominance relation      103 104
Dual      see bialgebra .19
Equivariant      140
Eulerian number      111
Foulkes character      111
Frame      53 71
Frame, column      54
Frame, connected      94
Frame, coupling      55 59 107
Frame, partition      54 72 84 144
Frame, row      54
Frame, semi-direct union      see union
Free Lie algebra      122
Frobenius, characteristic      28
Frobenius, lemma      135
Frobenius, reciprocity law      4 8 30 133
Gale      see Theorem
General linear group      123
Gessel      35 39
Graded      see algebra bialgebra homomorphism
Greene cell      68 86 156
Greene invariant      156
Group algebra      1
Group algebra, centre      135
Homogeneous component      127
Homomorphism of algebras      see algebra
Homomorphism of bialgebras      75 see
Homomorphism of coalgebras      see coalgebra
Homomorphism of modules      see module
Homomorphism, graded      75
Homomorphism, isometric      22 75
Hopf algebra      5
Horizontal strip      59 59 97
Ideal of a shape      see shape
Idempotent      129
Idempotent, central      129 135
Idempotent, orthogonal      129
Induction      132
Induction, rule      45 56 59 114
Inductive method      4
Irreducible      see character module
Isometric      see homomorphism
Joellenbeck      9
Joellenbeck algebra      55 58 71
Joellenbeck epimorphism      13
Klyachko      118
Klyachko, idempotent      118
Knuth      66 143
Kostka matrix      98 100 104
Kostka number      98 110
Kraskiewicz      see Theorem
Lattice permutation      109
Leclerc      see Theorem
Leeuwen      153
Leg length      91
Lehmann      116
Length of a word      21.

Lie algebra      see free Lie algebra
Lie module      123
Littlewood — Richardson rule      5 110
Mackey formula      7
MacMahon mapping      100 109
Main Theorem      12 75
Major index      118
Malvenuto      9 43
Maschke's Theorem      2 125
Matrix representation      4
Method, inductive      see inductive
Module, completely reducible      2
Module, homomorphism      126
Module, irreducible      2
Module, isomorphism      126
Module, multiplicity of an irreducible      129
Module, regular      2
Module, semi-simple      2
Module, Specht      4
Module, sub-      1
Module, trivial      131
Module, unital      1
Multiplicity      see module
Murnaghan-Nakayama Rule      93
Nakayama      see Murnaghan
Natural labeling      see shape
Noncommutative character      see character
Noncommutative cyclic character      121
Noncommutative irreducible character      13 72 107
Noncommutative orthogonality relations      12 72 145
Noncommutative regular character      13 86
Noncommutative symmetric functions      8
Opposite algebra      see algebra
Orthogonality relations      136
Orthogonality relations, noncommutative      see noncommutative
Outer product      see product
P-symbol      11 66
Partition      6
Partition conjugate      73 87 104
Partition frame      see frame
Permutation      3
Permutation, bialgebra of      see bialgebra
Picture      110
Plactic class      65 151 152
Plactic equivalence      65 143
Plactic monoid      66
Plactic neighbour      65 143
Polya action      45
Primitive element      10 61 75 77
Product, convolution      45
Product, outer on $\mathbb{C}$       26
Product, outer on $\mathbb{P}$       43 45
Q-symbol      11 66
Radical      72
Rearrangement      21
Reciprocity law      31 51
Reciprocity law, Frobenius'      see Frobenius
Reducible      see module
Regular      see character module bilinear
Representation      1 130
Representation matrix      4
Representation unital      1
Restriction      132
Restriction rule      48 58 59 108
Reutenauer      9 43 44 117
Rim hook      91 91 113
Robinson — Schensted correspondence      11 66 155
Row      see frame
Row in $\mathbb{Z} \times \mathbb{Z}$       36
Ruch      see Theorem
Ryser      see Theorem
Scalar product      3
Scharf      see Theorem
Schensted      see Theorem Robinson
Schonhofer      see Theorem
schur      28 123
Schur lemma      126
Schutzenberger      see Theorem
Self-dual      see bialgebra
Self-duality of $\mathbb{C}$       5 31
Self-duality of $\mathbb{P}$       10 51
Semi-direct      see union
Semi-simple      see algebra module
Set partition, ordered      139
Set partition, semigroup      140
Set partition, type      139
SHAPE      35
Shape, $\Pi$ -      36 38 41 43 46
Shape, ideal      41 48 91
Shape, isomorphism      35
Shape, natural labeling      35
Shape, sub-      41.
Skew character      see character
Solomon      6 7 58
Solomon epimorphism      7 63 78
Specht module      see module
Splitting field      3 85 137
Springer      121
Standard tableau      see tableau
Standard Young tableau      see tableau
Stanley      10 35
Sub-bialgebra      see bialgebra
Sub-coalgebra      see coalgebra
Sub-shape      see shape
Subalgebra      see algebra
Submodule      see module
Symmetric functions      28
Symmetric functions, noncommutative      8
Symmetric group      3
Tableau, standard      98 100 104
Tableau, standard Young      11 38 38 54 72 84 144 145 152 155
Tensor algebra      123
Theorem of Gale — Ryser      104
Theorem of Greene      156
Theorem of Klyachko      118
Theorem of Kraskiewicz — Weyman      121
Theorem of Leclerc — Scharf — Thibon      120
Theorem of Littlewood — Richardson      5 110
Theorem of Maschke      2 125
Theorem of Ruch — Schonhofer      104
Theorem of Schensted      73 157
Theorem of Schuetzenberger      12 66
Theorem of Wedderburn      129
Thibon      see Theorem
Thrall      123
Trace      2
Trivial character      see character
Trivial module      see module
TYPE      see set partition
Union, semi-direct      40 55
Unital      see representation module
Valley permutation      93
Wedderburn      see Theorem
Weyman      see Theorem
Word      6
Word, content      99
Word, permutation viewed as      3
Young      53
Young character      6 26 29 100 103 139
Young lattice      58
Young Rule      97
Young subgroup      6 26
Young tableau      see tableau
Zelevinski      5 110

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