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An Invitation to Representation Theory

Polynomial Representations of the Symmetric Group
BuchKartoniert, Paperback
229 Seiten
Englisch
Springererschienen am29.05.20221st ed. 2022
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.mehr
Verfügbare Formate
BuchKartoniert, Paperback
EUR37,44
E-BookPDF1 - PDF WatermarkE-Book
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Produkt

KlappentextIn 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.
Zusammenfassung
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
Details
ISBN/GTIN978-3-030-98024-5
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2022
Erscheinungsdatum29.05.2022
Auflage1st ed. 2022
ReiheSUMS Readings
Seiten229 Seiten
SpracheEnglisch
IllustrationenXV, 229 p.
Artikel-Nr.50444562

Inhalt/Kritik

Inhaltsverzeichnis
- 1. First Steps. - 2. Polynomials, Subspaces and Subrepresentations. - 3. Intertwining Maps, Complete Reducibility, and Invariant Inner Products. - 4. The Structure of the Symmetric Group. - 5. Sn-Decomposition of Polynomial Spaces for n = 1, 2, 3. - 6. The Group Algebra. - 7. The Irreducible Representations of Sn: Characters. - 8. The Irreducible Representations of Sn: Young Symmetrizers. - 9. Cosets, Restricted and Induced Representations. - 10. Direct Products of Groups, Young Subgroups and Permutation Modules. - 11. Specht Modules. - 12. Decomposition of Young Permutation Modules. - 13. Branching Relations.mehr
Kritik
"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)mehr

Autor

R. Michael Howe spent 20 years in various roles in the music industry and earned a PhD in mathematics at the University of Iowa, becoming a professor at the University of Wisconsin-Eau Claire, where he is now Emeritus Professor. As a mathematics professor he has supervised research and independent study projects of scores of undergraduate students, at least a dozen of whom have gone on to earn a PhD in mathematics. He still enjoys playing music and his other hobbies include hiking, mountaineering, kayaking, biking and skiing.
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Howe, R. Michael