Bruce E. SaganThe Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions (Graduate Texts in Mathematics, Vol. 203)

I'm a graduate student in mathematics, and I decided to take a qualifying examination in the area of Representation Theory, despite the fact that my high-level algebra experience is basically zero. To make matters worse the Professor for the topic, who is very highly acclaimed in the field, has no interest on lecturing on the the fundamentals of the theory. My entire class was feeling very frustrated as he lectured on about his areas of potential research without actually covering the underlying theory first.Thank god I found this book, which is very accessible, and provides three different approaches to the the topic. I highly recommend it.

Low stars not for the quality of writing, but because several of my pages were not bound. So there are pages falling out of my brand new book.

This is the book we use for my graduate combinatorics course. It's written quite well, especially for a graduate text.

This book is excellent. The material is presented clearly and concisely. It makes the subject matter accessible and interesting. I used it as the text for a one-semester graduate subject. I completed all of the exercises, so it is well-paced for this kind of study. I started with only an introductory knowledge of group theory, so it is self-contained. The only drawback is that there are no solutions to any of the exercises. If it had this, it would be a perfect bok.

Sagans book makes representation theory easy. The book first covers representations using modules and then choosing a basis to show the matrix approach. With every new topic he develops it using what Doron Zeilberger has dubbed the Gelfand Principle ([...]) The principle is: "Always chooses the smallest example to make a point". It isn't easy to find the smallest example when Sn grows as quickly as it does, but Sagen always manages to do it.The ensuing chapters follow in the same vein. Ideas are introduced and explained, sometimes with pictures, sometimes with calculations, but always as clearly as can be.To read this book does require a firm grounding in linear algebra, as well as abstract algebra. Time reading it is time well spent.

Very well-structures and well-explained. Says graduate but I'm an undergraduate with no background whatsoever in representation theory etc. (had never heard of modules) and had no problems understanden. Some parts at the beginning weren't as obvious to me as the book said cause we might not have covered it in Algebra courses or I just didn't recall but I managed to prove all these properties myself so that was actually good, gave me something to work on :) and if you don't wanna do this, I'm sure you can find it online easily.Super interesting and fun, easy to keep track of and very self-contained!

Das Buch behandelt sehr viele Fragen über die symmetrische Gruppe und gibt in den meisten Fällen explizite Konstruktionen, während sich andere Bücher meist nur Existenz und bestimmte Eigenschaften konzentrieren.Das Buch ist for allem geeigent für Leser die Kombinatorik mögen und es gerne explizit haben.

no puedo opinar, me censuran los censores de amazon.es

Not an original book

対称群は群の中でも代表的な群である. 群の表現論とは群の構造をベクトル空間に「埋め込む」ことで表現空間をつくり、その群や表現空間の内部構造を分析する学問である. この2つが合わさった時、あなたは「ヤング図形」という新たな概念を知る事になるだろう. 定義は至ってシンプルなのだが、今も様々な数学的現象を提供してくれる不思議な図形だ. この本はその「不思議さ」を我々に分かりやすく説明してくれる本である. Chapter.3のロビンソン-シェンステッド対応が「純粋な組合せ論」の立場から、対称群とヤング図形との関係を伝えてくれるのもポイントだろう. ただし、最近は「Okounkov-Vershik-approach」という、対称群の既約表現の新たな構成法が発見されたころである. 詳しくは「Representation Theory of the Symmetric Groups The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras. Cambridge 121」を見られたい.