Representation Theory: A First Course (Graduate Texts in Mathematics, 129)

This book is insanely huge and insanely in-depth. I'm still just barely skimming the surface of the material, but I'm loving the book itself. Great appendices to help the reader catch up with the basic material needed to undertake what's to come. Useful "solutions to selected problems" section. I love the lay-out of the sections, too. Every subject is broken up into manageable/digestible sections (or, at least, as manageable as a book on the subject can hope to be).I've never taken a course in Representation Theory, so I thought this might be a good book to check out to get the basics on a subject that I have some interest in pursuing more in depth at some point. Thankfully, that's exactly what the authours intended this book to be (they even say as much in the introduction)!I'm definitely plodding my way through the material, but it's a fun book to take a bit at a time on one's own time and at one's own pace. Honestly, if I were using this text in a class with a finite amount of time to cover the material, I'm pretty sure I'd feel overwhelmed because it IS dense and it DOES leave a lot "left to the reader" (that dreaded phrase!). But all in all, this struck me as one of the most solid and in-depth entry-level Representation Theory texts from the selection I perused before making a purchasing choice.

This is the book that seems to have everything. Written by two of the masters with such ambition as to cover representations of finite groups, representations of Lie algebras, together with countless detailed examples (and many pictures to boot!), what could go wrong?Within the first few pages, though, you should begin to feel that something is amiss. Proofs and arguments are almost always incomplete. Details are never provided under any circumstances. Example computations are beautiful and swift, but usually rely on an understanding that is deeper than actually presented in the text, using lemmas not present anywhere in the entire volume. They are the sorts of computations which, if included on a homework assignment and graded by someone well-versed in the subject, would get at most half the marks with several copies of the comment "yes, but you need to explain why." Nearly half the subject, you will realize after close analysis, is just left to the reader. The authors also supplement the instruction with an annoying delusion that the entire book is trivial; they will repeatedly tell you that everything here is trivial, easy, or immediate, but they will never acknowledge anything as being hard. Not only is this of course wrong, but it's disrespectful to their brilliant predecessors who toiled day and night to bring to them these apparently trivial truths.This is an exceptionally dangerous book to learn from. It's the sort of book that makes you think you understand the details when in fact you have no idea what you're talking about. It makes you think something's trivial or simple when it actually requires some clever thinking. Given the book's length, it is clear that the authors were simply too ambitious. One (or, evidently, two!) cannot cover this range of material in appropriate detail and with due care to the reader without violating all reasonable restrictions on how fat and bloated any single volume should permit itself to become before giving into gluttonous sin.This book isn't all bad, though. It makes a decent reference due to its ambition. There are some nice pictures. And the methods of computation really are nice--just don't think you understand them if you haven't written pages of extra notes filling in the gaps.Vinberg's Linear Representations of Groups is a much superior treatment of the basics of the subject. After using Fulton and Harris's book, you may be surprised to see how much more space it takes Vinberb to cover what Fulton and Harris annihilate in a few pages or even paragraphs here. And then you will realize how frail and weak the treatment of individual topics actually is in the present book.

I first read this book when I was transitioning from undergraduate to graduate school. It is example-driven and the general theory is difficult to find, but I think when coupled with a more theory-driven book like Humphreys' _Introduction to Lie Algebras and Representation Theory_ it can make a very nice companion. In fact, reading these two books is how I began to learn about representation theory of semisimple complex Lie algebras / groups.Some of the material (like Weyl's construction for irreducible representations of the orthogonal and symplectic groups) in Fulton-Harris is not readily found in other introductory books so I appreciated that it gave me exposure to topics that might otherwise only be found in research papers. Even after finishing my PhD (which did use the material in this book), I continue to find myself using this book as a reference.

I'm using this book as the text for one graduate course representation theory. This book is written in a modern fashion. Very good to take a survey of modern treatment of group representation. Futon and Harris use notations from category theory. At some place, they also use vector bundle. They assume readers have been familiar with those things. Means the author assume a high start point. Read Michael Artin's algebra as well as S. Lang's Algebra before you start this one would help a lot.The book I received is very new - newer than I expected.

This book is an excellent introduction to representation theory of finite groups, Lie groups and Lie algebras. It is easy to read, not too dense, contains many exercises, and spends a lot of time on examples before exposing the general theory. Probably my favorite intro to repn theory book.

The authors seem pretty good on Young's diagrams,but mostly as far as Cartan algebra, Lie algebraand representation theory they are pretty clueless.I spent way too much money buying this bookfor it to be this useless as a self-teaching tool.Since this is my 4th representation theory bookI have to say that these guys makeJean-Pierre Serre's book  Linear Representations of Finite Groups (Graduate Texts in Mathematics) (v. 42) look betterand makes a hero out of James E. Humphreys  Introduction to Lie Algebras and Representation Theory (Graduate Texts in Mathematics) .If you are buying a book by Fulton stick to algebraic geometryor intersection theory, maybe?

Great book. We are doing a reading group on it.

Requires a VERY GOOD knowledge of Linear Algebra. The proofs in the book understand you are hugely familiar with advanced concepts in it.

大変に分かりやすい表現論の入門書である。但し、分かりやすさ優先で書いたためか非常に分厚い。日本語で書かれた無料で読める資料としては京大の西山先生のテキストがあるのでそれも適宜参考にするのが良いだろう。