Representations of Groups: A Computational Approach (Cambridge Studies in Advanced Mathematics Book 124) 1st Edition by Klaus Lux (PDF)

Description

The representation theory of finite groups has seen rapid growth in recent years with the development of efficient algorithms and computer algebra systems. This is the first book to provide an introduction to the ordinary and modular representation theory of finite groups with special emphasis on the computational aspects of the subject. Evolving from courses taught at Aachen University, this well-paced text is ideal for graduate-level study. The authors provide over 200 exercises, both theoretical and computational, and include worked examples using the computer algebra system GAP. These make the abstract theory tangible and engage students in real hands-on work. GAP is freely available from www.gap-system.org and readers can download source code and solutions to selected exercises from the book’s web page.

User’s Reviews

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

⭐I’m still kind of a novice at representation theory, but in my math marathon to satisfy my curiosity about 2-modular representations of the symmetric group, this book been perfect!! The exercises are thoroughly engaging, whereby you can attain transcendent abandon without complete mastery of the definitions. It beats staring at a blank page, not knowing what to do, or waiting as your brain is still learning how to think about the definitions better. There are lots of pleasurable challenges, and the terseness never exceeds the heuristics. The GAP snippets will be great for when you want to get involved with the computer, which is one of the advantages of representations over finite fields that compensates for its being more advanced than ordinary representations. Which brings me to my next point. Ironically, for a book about advanced abstract computations, the most “obvious” thing that sensitive people notice about this _physical_ book is the spiritual energy, which is pure warmth. It’s currently the most warm math book in my library, although different books have occupied that distinction in the past. The questions posed in this book are of the utmost importance to humanity, and it’s up to you to apply it to your needs, and figure out why. The module-theoretic bias is of course a boon for things like induced representations, and some of it can also be applied to ordinary representations.

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