對稱群的表示論 (英文) (法)皮埃爾-洛伊克.梅利奧特 9787576706192 【台灣高等教育出版社】

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書名：對稱群的表示論 (英文)
ISBN：9787576706192
出版社：哈爾濱工業大學
著編譯者：(法)皮埃爾-洛伊克.梅利奧特
叢書名：國外優秀數學著作原版系列(第二十輯)
頁數：684
所在地：中國大陸 *此為代購商品
書號：1527429
可大量預訂，請先連絡。

內容簡介

本書包含了，對稱群與對稱函數、赫克代數及其表示、劃分的可觀測、隨機楊氏圖的模型等四部分，其中包含了，有限群的表示與半單代數、對稱函數與弗羅比尼烏斯-舒爾同構、劃分與表的組合、赫克代數與布饒爾-嘉當(Brauer—cartan)定理、赫克代數的特徵與對偶、q-0時的赫克代數特殊化的表示、可觀測的伊萬諾夫-克羅夫代數、朱西-墨菲元素、對稱群與自由概率、斯坦利-費雷公式與克羅夫多項式、無限對稱群的表示、中心測度的漸近數、普朗謝雷爾測度和舒爾-外爾測度的漸近等內容。

作者簡介

皮埃爾-洛伊克·梅利奧特，法國數學家，巴黎第十一大學教授。

目錄

preface
Ⅰ Symmetric groups and symmetric functions
1 Representations of finite groups and semisimple algebras
1 1 Finite groups and their representations
1 2 Characters and constructions on representations
1 3 The non-commutative Fourier transform
1 4 Semisimple algebras and modules
1 5 The double commutant theory
2 Symmetric functions and the Frobenius-Schur isomorphism
2 1 Conjugacy classes of the symmetric groups
2 2 The five bases of the algebra of symmetric functions
2 3 The structure of graded self-adjoint Hopf algebra
2 4 The Frobenius-Schur isomorphism
2 5 The Schur-Weyl duality
3 Combinatorics of partitions and tableaux
3 1 Pieri rules and Murnaghan-Nakayama formula
3 2 The Robinson-Schensted-Knuth algorithm
3 3 Construction of the irreducible representations
3 4 The hook-length formula
Ⅱ Hecke algebras and their representations
4 Hecke algebras and the Brauer-Cartan theory
4 1 Coxeter presentation of symmetric groups
4 2 Representation theory of algebras
4 3 Brauer-Cartan deformation theory
4 4 Structure of generic and specialized Hecke algebras
4 5 Polynomial construction of the q-Specht modules
5 Characters and dualities for Hecke algebras
5 1 Quantum groups and their Hopf algebra structure
5 2 Representation theory of the quantum groups
5 3 Jimbo-Schur-Weyl duality
5 4 Iwahori-Hecke duality
5 5 Hall-Littlewood polynomials and characters of Hecke algebras
6 Representations of the Hecke algebras specialized at q = 0
6 1 Non-commutative symmetric functions
6 2 Quasi-symmetric functions
6 3 The Hecke-Frobenius-Schur isomorphisms
Ⅲ Observables of partitions
7 The Ivanov-Kerov algebra of observables
7 1 The algebra of partial permutations
7 2 Coordinates of Young diagrams and their moments
7 3 Change of basis in the algebra of observables
7 4 Observables and topology of Young diagrams
8 The Jucys-Murphy elements
8 1 The Gelfand-Tsetlin subalgebra of the symmetric group algebra
8 2 Jucys-Murphy elements acting on the Gelfand-Tsetlin basis
8 3 Observables as symmetric functions of the contents
9 Symmetric groups and free probability
9 1 Introduction to free probability
9 2 Free cumulants of Young diagrams
9 3 Transition measures and Jucys-Murphy elements
9 4 The algebra of admissible set partitions
10 The Stanley-Feray formula for characters and Kerov polynomials
10 1 New observables of Young diagrams
10 2 The Stanley-Feray formula for characters of symmetric groups
10 3 Combinatorics of the Kerov polynomials
Ⅳ Models of random Young diagrams
11 Representations of the infinite symmetric group
11 1 Harmonic analysis on the Young graph and extremal characters
11 2 The bi-infinite symmetric group and the Olshanski semigroup
11 3 Classification of the admissible representations
11 4 Spherical representations and the Gelfand-Naimark-Segal cons-truction
12 Asymptoties of central measures
12 1 Free quasi-symmetric functions
12 2 Combinatorics of central measures
12 3 Gaussian behavior of the observables
13 Asymptotics of Plancherel and Schur-Weyl measures
13 1 The Plancherel and Schur-Weyl models
13 2 Limit shapes of large random Young diagrams
13 3 Kerov's central limit theorem for characters
Appendix
Appendix A Representation theory of semisimple Lie algebras
A 1 Nilpotent， solvable and semisimple algebras
A 2 Root system of a semisimple complex algebra
A 3 The highest weight theory
References
Index
編輯手記

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