Representation Theory of Symmetric Groups

Content: Cover
 Half Title
 Title Page
 Copyright Page
 Table of Contents
 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 algebra2.4 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 algebras4.5 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 observables7.1 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 elements9.4 The algebra of admissible set partitions
 10: The Stanley-Féray formula and Kerov polynomials
 10.1 New observables of Young diagrams
 10.2 The Stanley-Féray 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