Representation Theory of the Symmetric Groups
The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras
Seiten
2010
Cambridge University Press (Verlag)
978-0-521-11817-0 (ISBN)
Cambridge University Press (Verlag)
978-0-521-11817-0 (ISBN)
The representation theory of the symmetric groups is a classical topic that has grown into a huge body of theory, with many important connections to other areas of mathematics and physics. This self-contained introduction comprises classical and modern topics, including an exhaustive exposition of the new Okounkov–Vershik approach.
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.
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.
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.
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.
| Erscheint lt. Verlag | 4.2.2010 |
|---|---|
| Reihe/Serie | Cambridge Studies in Advanced Mathematics ; Vol.121 |
| Zusatzinfo | Worked examples or Exercises; 2 Tables, unspecified; 90 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Gewicht | 800 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 0-521-11817-4 / 0521118174 |
| ISBN-13 | 978-0-521-11817-0 / 9780521118170 |
| Zustand | Neuware |
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