Representation Theory of the Symmetric Groups: The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras (Cambridge Studies in Advanced Mathematics, Series Number 121) 1st Edition by Tullio Ceccherini-Silberstein (PDF)

Description

The representation theory of the symmetric groups is a classical topic that, since the pioneering work of Frobenius, Schur and Young, has grown into a huge body of theory, with many important connections to other areas of mathematics and physics. This self-contained book provides a detailed introduction to the subject, covering classical topics such as the Littlewood–Richardson rule and the Schur–Weyl duality. Importantly the authors also present many recent advances in the area, including Lassalle’s character formulas, the theory of partition algebras, and an exhaustive exposition of the approach developed by A. M. Vershik and A. Okounkov. A wealth of examples and exercises makes this an ideal textbook for graduate students. It will also serve as a useful reference for more experienced researchers across a range of areas, including algebra, computer science, statistical mechanics and theoretical physics.

User’s Reviews

Editorial Reviews: Review “This beautifully written new book is a welcome addition… It is almost entirely self-contained, only assuming some basic group theory and linear algebra, yet it takes one to the forefront of recent advances in the area. It would be entirely suitable for a single semester or year-long graduate course, as it is replete with examples and exercises of varying difficulty. I suspect it will also find its way on to the shelf as a valuable reference work for researchers in the field, as it is an excellent complement to books of Kleshchev, Sagan, James, and James and Kerber.” David John Hemmer, Mathematical Reviews Book Description A self-contained introduction to the representation theory of the symmetric groups, including an exhaustive exposition of the Okounkov–Vershik approach. About the Author Tullio Ceccherini-Silberstein is Professor in the Faculty of Engineering at the University of Sannio, Benevento.Fabio Scarabotti is Professor in the Faculty of Engineering at the University of Rome ‘La Sapienza’.Filippo Tolli is Associate Professor in the Department of Mathematics at Roma Tre University. Read more

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

⭐対称群の表現論は,１．対称関数の理論２．リー群やリー環の表現（主に古典群）３．Schur-Weyl（一般線形群の表現,テンソル積の直和分解）４．岩堀Hecke代数等のCoxeter性をもつ代数の構造や表現論などを議論するのに非常に重要な概念です. Bruce.E.Sagan先生の本は非常に分かりやすくまとまっており,今や対称群の表現論の標準的なテキストとして君臨しているほどです. しかし、この本はOkounkov-Vershik Approachという,Young-Jucy-Murphy-element（通称YJM）と有限群の離散フーリエ解析を用いた対称群の既約表現の導出が詳しく書かれております.（Section3‾1からSection3‾3まで）後はヤング半正規形,murnaghan-Nakayama-rule,Kostka数,そしてSchur関数等の対称関数の理論…といったように対称群の表現論の内容や応用をよく盛り込んでいます. 終盤に一般線形群の表現への応用が書かれているのもGOOD.（上記の3にあたります.） ただ,Section1では「有限群の表現論」と書かれてはいるものの, この本から有限群の表現論「のみ」を学ぶのはおすすめしません.（J.P.SerreやGordon.Jamesの本などが良いと思う.） あくまでも「対称群」の為の準備だと思ったほうがいいでしょう. また,初版なのか,誤植も少しあります.（ページが進む毎にやや多くなってる？） しかし, しっかり読めば群の表現論の面白さを対称群を通して知ることができると思います. どうせならSagan先生の本と一緒に読んでみるのも一興でしょう. ただ総合的に例があまり多くないので、読む際には自分で例を作ってみて実験することを勧めます. そうした方がよく理解できますので.追記, Section6のLittlewood-Richardson-ruleとその応用であるSpecht-moduleの一般化はB.E.SaganのChapter.2を拡張したような構成になっていますので, いっそのこと併読をおすすめします.

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Free Download Representation Theory of the Symmetric Groups: The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras (Cambridge Studies in Advanced Mathematics, Series Number 121) 1st Edition in PDF format
Representation Theory of the Symmetric Groups: The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras (Cambridge Studies in Advanced Mathematics, Series Number 121) 1st Edition PDF Free Download
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Representation Theory of the Symmetric Groups: The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras (Cambridge Studies in Advanced Mathematics, Series Number 121) 1st Edition 2010 PDF Free Download
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