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

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: February 2010
  • availability: Available
  • format: Hardback
  • isbn: 9780521118170


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About the Authors
  • 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.

    • 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
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    Product details

    • Date Published: February 2010
    • format: Hardback
    • isbn: 9780521118170
    • length: 430 pages
    • dimensions: 229 x 152 x 29 mm
    • weight: 0.8kg
    • contains: 90 b/w illus. 2 tables 80 exercises
    • availability: Available
  • Table of Contents

    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

  • Authors

    Tullio Ceccherini-Silberstein, Università degli Studi del Sannio
    Tullio Ceccherini-Silberstein is Professor in the Faculty of Engineering at the University of Sannio, Benevento.

    Fabio Scarabotti, Università degli Studi di Roma 'La Sapienza', Italy
    Fabio Scarabotti is Professor in the Faculty of Engineering at the University of Rome 'La Sapienza'.

    Filippo Tolli, Università degli Studi Roma Tre, Italy
    Filippo Tolli is Associate Professor in the Department of Mathematics at Roma Tre University.

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