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

A self-contained introduction to the representation theory of the symmetric groups, including an exhaustive exposition of the Okounkov–Vershik approach.

Tullio Ceccherini-Silberstein (Author), Fabio Scarabotti (Author), Filippo Tolli (Author)

9780521118170, Cambridge University Press

Hardback, published 4 February 2010

430 pages, 90 b/w illus. 2 tables 80 exercises
22.9 x 15.2 x 2.9 cm, 0.8 kg

"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 Reviews

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.

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.

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