Representation Theory of the Symmetric Groups : The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras (Cambridge Studies in Advanced Mathematics)

Ceccherini-Silberstein, Tullio/ Scarabotti, Fabio/ Tolli, Filippo

Cambridge University Press（2010/02発売）

• 製本 Hardcover:ハードカバー版／ページ数 430 p.／サイズ 90 b/w illus.
• 言語 ENG
• 商品コード 9780521118170
• DDC分類 512.2

基本説明

Serves as a useful reference for researchers across a range of subjects, including algebra, computer science and statistical mechanics.

Full 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.

Contents

Preface; 1. Representation theory of finite groups; 2. The theory of Gelfand-Tsetlin bases; 3. The Okounkov-Vershik approach; 4. Symmetric functions; 5. Content evaluation and character theory; 6. The Littlewood-Richardson rule; 7. Finite dimensional *-algebras; 8. Schur-Weyl dualities and the partition algebra; Bibliography; Index.