Representation Theory of the Symmetric Groups

Representation Theory of the Symmetric Groups : The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras

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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.show more

Product details

  • Online resource
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 90 b/w illus. 2 tables 80 exercises
  • 1139192361
  • 9781139192361

Table of 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.show more

About Tullio Ceccherini-Silberstein

Tullio Ceccherini-Silberstein is Professor in the Faculty of Engineering at the University of Sannio, Benevento. Fabio Scarabotti is Professor in the Faculty of Engineering at the University of Rome 'La Sapienza'. Filippo Tolli is Associate Professor in the Department of Mathematics at Roma Tre University.show more

Review quote

"This beautifully written new book is a welcome addition... It is almost entirely self-contained, only assuming some basic group theory and linear algebra, yet it takes one to the forefront of recent advances in the area. It would be entirely suitable for a single semester or year-long graduate course, as it is replete with examples and exercises of varying difficulty. I suspect it will also find its way on to the shelf as a valuable reference work for researchers in the field, as it is an excellent complement to books of Kleshchev, Sagan, James, and James and Kerber." David John Hemmer, Mathematical Reviewsshow more