Representation Theory of Symmetric Groups

Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint.



This book is an excellent way of introducing today’s students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial algebras like the Iwahori-Hecke algebra.



In a clear and concise manner, the author presents the case that most calculations on symmetric group can be performed by utilizing appropriate algebras of functions. Thus, the book explains how some Hopf algebras (symmetric functions and generalizations) can be used to encode most of the combinatorial properties of the representations of symmetric groups.



Overall, the book is an innovative introduction to representation theory of symmetric groups for graduate students and researchers seeking new ways of thought.

1124106508
Representation Theory of Symmetric Groups

Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint.



This book is an excellent way of introducing today’s students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial algebras like the Iwahori-Hecke algebra.



In a clear and concise manner, the author presents the case that most calculations on symmetric group can be performed by utilizing appropriate algebras of functions. Thus, the book explains how some Hopf algebras (symmetric functions and generalizations) can be used to encode most of the combinatorial properties of the representations of symmetric groups.



Overall, the book is an innovative introduction to representation theory of symmetric groups for graduate students and researchers seeking new ways of thought.

61.99 In Stock
Representation Theory of Symmetric Groups

Representation Theory of Symmetric Groups

by Pierre-Loic Meliot
Representation Theory of Symmetric Groups

Representation Theory of Symmetric Groups

by Pierre-Loic Meliot

Paperback

$61.99 
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Overview

Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint.



This book is an excellent way of introducing today’s students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial algebras like the Iwahori-Hecke algebra.



In a clear and concise manner, the author presents the case that most calculations on symmetric group can be performed by utilizing appropriate algebras of functions. Thus, the book explains how some Hopf algebras (symmetric functions and generalizations) can be used to encode most of the combinatorial properties of the representations of symmetric groups.



Overall, the book is an innovative introduction to representation theory of symmetric groups for graduate students and researchers seeking new ways of thought.


Product Details

ISBN-13: 9781032476926
Publisher: CRC Press
Publication date: 01/21/2023
Series: Discrete Mathematics and Its Applications
Pages: 682
Product dimensions: 6.12(w) x 9.19(h) x (d)

Table of Contents



I Symmetric groups and symmetric functions



Representations of finite groups and semisimple algebras



Finite groups and their representations



Characters and constructions on representations



The non-commutative Fourier transform



Semisimple algebras and modules



The double commutant theory



Symmetric functions and the Frobenius-Schur isomorphism



Conjugacy classes of the symmetric groups



The five bases of the algebra of symmetric functions



The structure of graded self-adjoint Hopf algebra



The Frobenius-Schur isomorphism



The Schur-Weyl duality



Combinatorics of partitions and tableaux



Pieri rules and Murnaghan-Nakayama formula



The Robinson-Schensted-Knuth algorithm



Construction of the irreducible representations



The hook-length formula



II Hecke algebras and their representations



Hecke algebras and the Brauer-Cartan theory



Coxeter presentation of symmetric groups



Representation theory of algebras



Brauer-Cartan deformation theory



Structure of generic and specialised Hecke algebras



Polynomial construction of the q-Specht modules



Characters and dualities for Hecke algebras



Quantum groups and their Hopf algebra structure



Representation theory of the quantum groups



Jimbo-Schur-Weyl duality



Iwahori-Hecke duality



Hall-Littlewood polynomials and characters of Hecke algebras



Representations of the Hecke algebras specialised at q = 0



Non-commutative symmetric functions



Quasi-symmetric functions



The Hecke-Frobenius-Schur isomorphisms



III Observables of partitions



The Ivanov-Kerov algebra of observables



The algebra of partial permutations



Coordinates of Young diagrams and their moments



Change of basis in the algebra of observables



Observables and topology of Young diagrams



The Jucys-Murphy elements



The Gelfand-Tsetlin subalgebra of the symmetric group algebra



Jucys-Murphy elements acting on the Gelfand-Tsetlin basis



Observables as symmetric functions of the contents



Symmetric groups and free probability



Introduction to free probability



Free cumulants of Young diagrams



Transition measures and Jucys-Murphy elements



The algebra of admissible set partitions



The Stanley-Féray formula and Kerov polynomials



New observables of Young diagrams



The Stanley-Féray formula for characters of symmetric groups



Combinatorics of the Kerov polynomials



IV Models of random Young diagrams



Representations of the infinite symmetric group



Harmonic analysis on the Young graph and extremal characters



The bi-infinite symmetric group and the Olshanski semigroup 



Classification of the admissible representations



Spherical representations and the GNS construction



Asymptotics of central measures



Free quasi-symmetric functions



Combinatorics of central measures



Gaussian behavior of the observables



Asymptotics of Plancherel and Schur-Weyl measures



The Plancherel and Schur-Weyl models


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