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

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。

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.

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

Es ist das Werk, das den Horizont erweitert!

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.