Representation Theory of the Symmetric Groups
Representation Theory of the Symmetric Groups
Fabio Scarabotti , Università degli Studi di Roma 'La Sapienza', Italy
Filippo Tolli , Università degli Studi Roma Tre, Italy
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USDThe 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.
- Covers results and theories in a topic that has fruitful relations with many areas of mathematics and physics
- Was the first book to contain a complete treatment of the Okounkov–Vershik theory
- Serves as a useful reference for researchers across a range of subjects, including algebra, computer science and statistical mechanics
Reviews & endorsements
"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
Product details
March 2010Hardback
9780521118170
430 pages
229 × 152 × 29 mm
0.8kg
90 b/w illus. 2 tables 80 exercises
Available
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.
