Representations and Characters of Groups 2nd Edition by Gordon James (PDF)

Description

This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside’s paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.

User’s Reviews

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

⭐This is a nice book for undergraduates. You should know some group theory first and it would be helpful to know what modules are and what they are used for. If you don’t understand modules, read a few pages in Dummitt & Foote, or something like that. Wikipedia is even good for that. For anybody (such as theoretical physicists) wanting to understand representation theory in the way mathematicians view it, it’s the right type of book to read first before stuff like Fulton.

⭐The authors have ironed out some inconsistencies in the standard mathematical presentations. This makes things both easier and harder to understand – easier because it is internally more consistent, and harder because it’s harder to relate to other texts. But the way material is presented is very good. I have the Kindle version and I’m also ordering the paperback.

⭐Great book

⭐This is a great book. Well written and the copy I bought was in great condition

⭐Not having a formal background inpure mathematics, I approached thesubject of the representation theoryof finite groups with some trepidation.Having looked at various books in thefield, I found that the book byJames and Liebeck was the clearestand most readable exposition ofthe subject.There is little fuss or abstractformalism that might obscure themeaning of the fundamental conceptsand theorems. The material is clearlywritten and very well organized.The chapters are very short, thankfully,and the best thing is that there arecomplete worked solutions to all thechapter exercises.The book ends with a nice applicationof the theory to molecular vibration.(As always, it helps to know the basicfacts about groups, and linear algebra -vector spaces, linear transformations,matrices etc.)An excellent book!

⭐Unreadable because of ugly notation. It could be terrific book but they killed it.

⭐James and Liebeck have done a wonderful job presenting the material in a concise, straightforward, easily handled fashion. The book is well organized, the exercises vary from basic to difficult, and the solutions are provided in the back of the book so that you don’t have to bang your head on the wall for too long because of the tough problems!

⭐an excellent introductory text on GRT. answers in the back to all exercises make it ideal for self-study.

⭐* PhysicalThe paper is cream coloured, with the text of a fair size. it’s well bound too.* prerequisites?This book explains the theoretical supporting information underpinning matrices and its algebra within Group Theory. This is a differing approach as matrices within matrices to this area but enjoyable. The theory is very well explained too, but you need to go over it time and time again, so don’t expect it to open up without serious study. Its been very helpful in places to read this, but it won’t carry all you need to know to do this level of math. So, If you can get your hands on the now defunct Open University ‘M203: A Course in Pure Mathematics’ that covers the Group theory Block, this will be a great help. Specifically, Permutations, Cosets and Lagrange’s Theorem, Conjugacy, Isomorphisms and Homomorphisms, and Group Actions. This will attack this prerequisite area differently and help your reading of these same topics and beyond in this book. Another recommendation is to use – Youtube – and look at videos on Groups Theory and choose to rewatch to your understanding. This is VERY important to use these resources as it can be easier to comprehend, such as the Open University videos for example. There are other videos available from academic sources too.I have managed to read the book in its entirety and it has been helpful as bits of concepts click into place and my comprehension has broadened and widened. I need to go over this book again a few times and it been great so far.One of the unique features of this book is the relationship of chemistry to groups theory. This was I understood the math, but the chemistry left me stuck as I haven’t studied this topic much. Its on my reading list to eventually amend this!* SummaryI have read three or more books in this area and its a modern math with serious levels of abstraction and detail to go through. Quite how much of this is the detail for detail’s sake has yet to be determined. It’s not the ultimate book on this topic, but at least I have managed to stick with this book and read it all and its a platform to build upon in a more complex manner. Also, need to say that I haven’t grasped everything this book explains, so it’s not an easy book to understand (I.M.H.O)

⭐There is no doubt this is excellent as an introductory Representation Theory book: the material is presented in a straightforward and concise manner, and the authors have taken a lot of care in introducing the concepts as clearly as possible, with few prerequisites. I have previously tried to read another book on the subject, (“Linear Representations of Finite Groups” by J-P. Serre), but found it very difficult to follow and understand. The exercises are carefully selected, addressing most of the misunderstandings that may occur, and I found them very instructive.However, the major drawback of the book (at least for me) is the notation: in most/all contexts, the authors use rather unintuitive (and at times annoying) ones, such as right actions, multiplying permutations from left to right, writing linear transformations by multiplying the corresponding matrix to the right etc. They even place the function AFTER the argument in the homomorphisms (which is similar to writing (x)f instead of f(x), for a function f). While I understand the notation needs to be consistent and provides a few small advantages at times, I found myself struggling in some topics just because at some point I would forget to convert the notation to the familiar form when I was writing stuff down. It becomes almost automatic after a while, but I still don’t like to put in additional effort, considering that the course notes at my university (and many others) adopt the ‘usual’ order. For people who care about this, the book is really a hit or miss (but more of a hit either way – it does an amazing job of pointing out the key concepts and helping you remember them).

⭐I found the book easy to start with a cursory cursory read through to get an overview. I needed to re-read each chapter carefully to get to grips with the content. The contents fared well under scrutiny with neat concise proofs. Whether my linear algebra and group theory would stand the strain was always a worry, but the style of the writing kept me reassured, a compliment to the authors. The result is that I now have a fairly good idea of the subject.An enjoyable learning experience!

⭐excellent

⭐予備知識が線形代数（と集合論の初歩的知識）だけで十分なぐらい非常に分かりやすく書かれております. まず,群論や加群の基礎的内容から始まり,有限群の表現論を例をしつこく挙げながら説明しています. （むしろ有限群からの群環の理論っぽいですが, これは表現と「同一視」できることが知られています.）そしてシューアの補題（これがなければ表現論の研究は進まなかったと言ってよい.）,指標の理論(表現を「分類」するのに必要不可欠な概念.),既約表現への直和分解(特に群の「位数」や「可換性」と深い関わりがある.),具体的な群の指標表（やたらと力が入っているのは気のせいでしょうか.）,誘導表現(既存の表現から新しい表現を創り出す.),フロベニウス・シューア表示（群の表現が「実数上の」表現に実現できるかどうかを判定する. これも群論が関わっている.）,..など, 内容が豊富にあります. 終盤は著者が指標「マニア」なのかと思ってしまうくらいの理論であり, 例えばp-群やリー型の有限群の指標を求めようとしております. また, 最後には物理（バネの運動.）や化学（分子の対称性.）等の応用も紹介してくれています. 各節の最後にまとめが載っているのもGOOD. このように有限群の性質を表現を通して知りたい人には是非おすすめしたい良書である, と確信しています. ただし, 写像や加群の記号の書き方がやや古風（右側から詰めて書いている.）であり, 上述したようにかなり「しつこく」説明している本なので, 人によっては鼻につくかも知れません. 逆にこの2点が気にならないなら大丈夫ということです.

⭐

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