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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. An important highlight of this book is an innovative treatment of the Robinson–Schensted–Knuth correspondence and its dual by extending Viennot's geometric ideas. Another unique feature is 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 very 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. In addition, each exercise is assigned a difficulty level to test readers' learning. Solutions and hints to most of the exercises are provided at the end.Read more
- Follows a geometric, modern and accurate approach to the subject
- Presents detailed discussion on symmetric functions and polynomial representations of general linear groups, in separate chapters
- Provides solutions to selected problems
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- Date Published: February 2015
- format: Hardback
- isbn: 9781107082052
- length: 202 pages
- dimensions: 237 x 159 x 15 mm
- weight: 0.46kg
- availability: Available
Table of Contents
List of tables
1. Basic concepts of representation theory
2. Permutation representations
3. The RSK correspondence
4. Character twists
5. Symmetric functions
6. Representations of general linear groups
Hints and solutions to selected exercises
Suggestions for further reading
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