Representations of Finite and Compact Groups (Graduate Studies in Mathematics ; V. 10) by Barry Simon (PDF)

Description

Barry Simon, I.B.M. Professor of Mathematics and Theoretical Physics at the California Institute of Technology, is the author of several books, including such classics as Methods of Mathematical Physics (with M. Reed) and Functional Integration and Quantum Physics. This new book, based on courses given at Princeton, Caltech, ETH-Zurich, and other universities, is an introductory textbook on representation theory. According to the author, “Two facets distinguish my approach. First, this book is relatively elementary, and second, while the bulk of the books on the subject is written from the point of view of an algebraist or a geometer, this book is written with an analytical flavor”. The exposition in the book centers around the study of representation of certain concrete classes of groups, including permutation groups and compact semisimple Lie groups. It culminates in the complete proof of the Weyl character formula for representations of compact Lie groups and the Frobenius formula for characters of permutation groups. Extremely well tailored both for a one-year course in representation theory and for independent study, this book is an excellent introduction to the subject which, according to the author, is unique in having “so much innate beauty so close to the surface”.

User’s Reviews

Editorial Reviews: Review “Contains a very good explanation of representation theory of finite and compact groups and can be recommended to everyone for learning or teaching representation theory.” — Zentralblatt fr Mathematik”This book closes a gap that impeded instruction in the principles of the theory of group representations in the past … it would also tend to close the gap between the interested student of the subject and the advanced researcher keen on bare facts … a most readable account of a subject of enduring fascination.” — Monatshefte fr Mathematik”This is indeed a nice book … I would recommend it precisely for the graduate course [that] I am teaching now, “Representation Theory” … I very much like the hands-on approach and the very explicit formulae that are given … Professor Simon has done an excellent job on this beautiful material.” — Tudor Ratiu, University of California — Tudor Ratiu, University of California, Santa CruzCan be recommended as a base for courses about representations of finite groups and finite-dimensional representations of Lie groups. — Mathematical Reviews About the Author Barry Simon, I.B.M. Professor of Mathematics and Theoretical Physics at the California Institute of Technology, is the author of several books, including such classics as Methods of Mathematical Physics (with M. Reed) and Functional Integration and Quantum Physi

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is an excellent treatment of representation theory, especially focusing on the concrete problem of characterizing all the irreducible representations for some specific important groups such as SU(n) and the symmetric groups S_n. It gets to the point fast. One nice feature is that the book feels as if it is written for analysts and mathematical physicists who need to understand representations, but may not have the strongest background in algebra. The book is entirely self-contained, including all necessary background in algebra such as the Sylow theorems.

⭐Math books are usually difficult to read. This book is no exception. But it teaches the right material, at the right pace. It has been an invaluable part of my library.

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