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Introduction to Representation Theory
Pavel Etingof, Massachusetts Institute of Technology, Cambridge, MA, Oleg Golberg, Sebastian Hensel, Universität Bonn, Germany, Tiankai Liu, Massachusetts Institute of Technology, Cambridge, MA, Alex Schwendner, Two Sigma Investments, New York, NY, Dmitry Vaintrob, Harvard University, Cambridge, MA, and Elena Yudovina, University of Cambridge, United Kingdom
with historical interludes by Slava Gerovitch, Massachusetts Institute of Technology, Cambridge, MA
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Student Mathematical Library
2011; 228 pp; softcover
Volume: 59
ISBN-10: 0-8218-5351-1
ISBN-13: 978-0-8218-5351-1
List Price: US$42
Institutional Members: US$33.60
All Individuals: US$33.60
Order Code: STML/59
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Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory.

The goal of this book is to give a "holistic" introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints.

The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

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Readership

Undergraduate and graduate students interested in algebra and representation theory.

Reviews

"Add to this the sets of problems included in the book, replete with occasional hints and estimates of the degree of difficulty, as well as the wonderful 'Historical Interludes' by Slava Gerovitch, and the result is a fantastic little book. I think it is bound to become the way to get into this subject 'holistically.'"

-- MAA Reviews

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