An Invitation to Representation Theory

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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.

Über den 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.

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

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.

Details

Erscheinungsjahr:	2022
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	248
Reihe:	SUMS Readings
Inhalt:	xv 229 S.
ISBN-13:	9783030980245
ISBN-10:	3030980243
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Howe, R. Michael
Auflage:	1st ed. 2022
Hersteller:	Springer International Publishing SUMS Readings
Maße:	235 x 155 x 14 mm
Von/Mit:	R. Michael Howe
Erscheinungsdatum:	29.05.2022
Gewicht:	0,382 kg

preigu-id: 121173011