An Invitation to Representation Theory

Beschreibung

An Invitation to Representation Theory offers an introduction to groups and their representations, suitable for undergraduates. In this book, the ubiquitous symmetric group and its natural action on polynomials are used as a gateway to representation theory.
The subject of representation theory is one of the most connected in mathematics, with applications to group theory, geometry, number theory and combinatorics, as well as physics and chemistry. It can however be daunting for beginners and inaccessible to undergraduates. The symmetric group and its natural action on polynomial spaces provide a rich yet accessible model to study, serving as a prototype for other groups and their representations. This book uses this key example to motivate the subject, developing the notions of groups and group representations concurrently.
With prerequisites limited to a solid grounding in linear algebra, this book can serve as a first introduction to representation theory at the undergraduate level, for instance in a topics class or a reading course. A substantial amount of content is presented in over 250 exercises with complete solutions, making it well-suited for guided study.
An Invitation to Representation Theory offers an introduction to groups and their representations, suitable for undergraduates. In this book, the ubiquitous symmetric group and its natural action on polynomials are used as a gateway to representation theory.
The subject of representation theory is one of the most connected in mathematics, with applications to group theory, geometry, number theory and combinatorics, as well as physics and chemistry. It can however be daunting for beginners and inaccessible to undergraduates. The symmetric group and its natural action on polynomial spaces provide a rich yet accessible model to study, serving as a prototype for other groups and their representations. This book uses this key example to motivate the subject, developing the notions of groups and group representations concurrently.
With prerequisites limited to a solid grounding in linear algebra, this book can serve as a first introduction to representation theory at the undergraduate level, for instance in a topics class or a reading course. A substantial amount of content is presented in over 250 exercises with complete solutions, making it well-suited for guided study.
First text accessible to undergraduates having taken a course in linear algebra Contains over 250 exercises with complete solutions Introduces many important notions of algebra

Autor*in

R. Michael Howe

Themen in »An Invitation to Representation Theory«

Undergraduate Representation Theory Symmetric Group Group Actions Young Tableaux Young Diagrams Young Symmetrizers Representation Theory of the Symmetric Group Polytabloids Branching Specht Module Induced Representations

Stimmen zu »An Invitation to Representation Theory«

“The book under review is a nice introduction to the representation theory of the symmetric group. … The book is well structured and enriched with numerous exercises, many of which are solved or with hints for the solution.” (Enrico Jabara, zbMATH 1514.20002, 2023)
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