Description
Book SynopsisThis 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 RobinsonSchenstedKnuth 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 SchurWeyl 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.
Table of ContentsList 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.
