Representation Theory of Symmetric Groups 1st Edition by Pierre-Loic Meliot ISBN 978-1498719124 1498719120

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Product details: 

ISBN 10:  1498719120

ISBN 13: 978-1498719124

Author:  Pierre-Loic Meliot

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.

Table of contents: 

Part 1: Symmetric Groups and Symmetric Functions (145 pages)
Chapter 1: Representations of Finite Groups and Semisimple Algebras (46 pages)

Chapter 2: Symmetric Functions and the Frobenius–Schur Isomorphism (50 pages)

Chapter 3: Combinatorics of Partitions and Tableaux (47 pages)

Part 2: Hecke Algebras and Their Representations (178 pages)
Chapter 4: Hecke Algebras and the Brauer–Cartan Theory (68 pages)

Chapter 5: Characters and Dualities for Hecke Algebras (70 pages)

Chapter 6: Representations of the Hecke Algebras Specialized at q = 0 (38 pages)

Part 3: Observables of Partitions (174 pages)
Chapter 7: The Ivanov–Kerov Algebra of Observables (48 pages)

Chapter 8: The Jucys–Murphy Elements (26 pages)

Chapter 9: Symmetric Groups and Free Probability (50 pages)

Chapter 10: The Stanley–Féray Formula for Characters and Kerov Polynomials (48 pages)

Part 4: Models of Random Young Diagrams (129 pages)
Chapter 11: Representations of the Infinite Symmetric Group (46 pages)

Chapter 12: Asymptotics of Central Measures (48 pages)

Chapter 13: Asymptotics of Plancherel and Schur–Weyl Measures (33 pages)

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Tags: Pierre Loic Meliot, Representation Theory, Symmetric Groups