Representation Theory of Symmetric Groups PDF

Features

Uses the newest research studies and results for the new generation of researchers and students of combinatorics, algebra and discrete mathematics

Examines representations of symmetric groups and symmetric functions

Presents observables of partitions and the dual approach to representation theory

Studies models of random partitions stemming from representation theory

Summary

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.

Author: Pierre-Loic Meliot