Representation theory of the symmetric groups
Subtitle: the Okounkov-Vershik approach, character formulas, and partition algebras
By: Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli.
Contributors: Scarabotti, Fabio.; Tolli, Filippo, 1968-
Series: Cambridge studies in advanced mathematics -- 121
Publisher: Cambridge University Press
Published: 2010
Place of publication: New York
Language: eng
Number of pages: 412
ISBN-13: 9780521118170
Subjects: Symmetry groups; Representations of groups
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"--Provided by publisher.
Notes: Includes bibliographical references and index.
Table of contents: title: Machine generated contents note: 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.