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Can you recommend me book of problems in representation theory of finite group with solutions (or answers).


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up vote 6 down vote accepted

Pavel Etingof at MIT just published a new book on the subject in the AMS's Student Mathematical Library based on his honors course for undergraduates and graduate students at MIT. It's very up-to-date,more so then the classical books on the subject and contains a host of exercises. The pedigree alone should make this a book worth having-and best of all, the preliminary version is available for free online at Etingof's website.

James and Liebek's book mentioned below is somewhat gentler and more wordy-it's probably better for self study. It's a really nice book in the spirit of the great British algebra books like Rose and Cohn.

And of course I'd be derelict in my duty if I didn't mention 2 great classics on the subject: J.P. Serre's LINEAR REPRESENTATIONS OF FINITE GROUPS and Schlomo Sternberg's GROUPS AND PHYSICS. Both contain all the basics and a host of great problems-and best of all,both contain applications to physics and chemistry of this beautiful subject. Sternberg's book also contains fascinating historical notes of the subject in both mathematics and physics, including Sternberg's own experiences as a student at Harvard with the legendary George Mackey. These alone make the book worth having!

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Is there Pavel Etingof's book somewhere on free access in www? – Aspirin Sep 19 '11 at 1:32
A preliminary draft can be found here: But keep in mind it's much shorter and less polished then the finished book. That being said-you can certainly use it to see if the finished version is worth the money. – Mathemagician1234 Sep 19 '11 at 3:18
The book isn't just by Etingof: also Golberg, Hensel, Liu, Schwendner, Vaintrob, Yudovina and Gerovitch – m_t_ Sep 27 '12 at 7:40

I recommend Representations and Characters of Groups by James and Liebek. It is not a list of problems, but rather a textbook. However, the entire book is about finite groups, I believe, and every exercise in the book has a solution in the end.

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This and Etingof's books are probably the best books for self study on the subject,William. – Mathemagician1234 Oct 6 '11 at 4:24

The first part of Fulton and Harris's book "Representation theory : a first course" is about the representation theory of finite groups. It has a large number of very good exercises, and solutions to the more difficult ones are in the back of the book.

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