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Representation theory. A combinatorial viewpoint. (English) Zbl 1331.20007

Cambridge Studies in Advanced Mathematics 147. Cambridge: Cambridge University Press (ISBN 978-1-107-08205-2/hbk; 978-1-139-97682-4/ebook). xii, 192 p. (2015).
This book discusses the representation theory of symmetric groups, the theory of symmetric functions and the polynomial representation theory of general linear groups.
The first chapter provides a detailed account of necessary representation-theoretic background for finite groups. An innovative treatment of the Robinson-Schensted-Knuth correspondence and its dual are given in Chapter 2. The author gives an exposition of the relationship between these correspondences, the representation theory of symmetric groups and alternating groups and the theory of symmetric functions. Schur algebras are introduced naturally as algebras of distributions on general linear groups. The treatment of Schur-Weyl duality reveals the directness and simplicity of Schur’s original treatment of the subject. – This book is a helpful reference for any beginners who are interested in learning combinatorial representation theory.
Reviewer: Hu Jun (Beijing)

MSC:

20C15 Ordinary representations and characters
20G05 Representation theory for linear algebraic groups
05E10 Combinatorial aspects of representation theory
20-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory
20C30 Representations of finite symmetric groups
05E05 Symmetric functions and generalizations
20G43 Schur and \(q\)-Schur algebras
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