Representation Theory
A Combinatorial Viewpoint

This book discusses representation theory of symmetric groups, theory of symmetric functions and polynomial representation theory of general linear groups.

Amritanshu Prasad (Author)

9781107082052, Cambridge University Press

Hardback, published 5 February 2015

202 pages
23.7 x 15.9 x 1.5 cm, 0.46 kg

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.

List of tables
Preface
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
References
Index.

Subject Areas: Algebra [PBF], Discrete mathematics [PBD], Mathematics [PB]