Linear and Projective Representations of Symmetric Groups

Kleshchev describes a new approach to the subject of the representation theory of symmetric groups.

Alexander Kleshchev (Author)

9780521104180, Cambridge University Press

Paperback / softback, published 19 March 2009

292 pages
22.9 x 15.2 x 1.7 cm, 0.43 kg

"The book is written with great care and in a dense style... The author has mastered a very difficult task in writing this book and has enriched the literature on the symmetric groups with a unique and very valuable monograph, making the formidable recent developments more widely accessible by starting the presentation from scratch."
Christine Bessenrodt, Mathematical Reviews

The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics such as combinatories, Lie theory and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own. Much of this work has previously appeared only in the research literature. However to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract algebra. For the sake of transparency, Kleshchev concentrates on symmetric and spin-symmetric groups, though methods he develops are quite general and apply to a number of related objects. In sum, this unique book will be welcomed by graduate students and researchers as a modern account of the subject.

Preface
Part I. Linear Representations: 1. Notion and generalities
2. Symmetric groups I
3. Degenerate affine Hecke algebra
4. First results on Hn modules
5. Crystal operators
6. Character calculations
7. Integral representations and cyclotomic Hecke algebras
8. Functors e and f
9. Construction of Uz and irreducible modules
10. Identification of the crystal
11. Symmetric groups II
Part II. Projective Representations: 12. Generalities on superalgebra
13. Sergeev superalgebras
14. Affine Sergeev superalgebras
15. Integral representations and cyclotomic Sergeev algebras
16. First results on Xn modules
17. Crystal operators fro Xn
18. Character calculations for Xn
19. Operators e and f
20. Construction of Uz and irreducible modules
21. Identification of the crystal
22. Double covers
References
Index.

Subject Areas: Algebra [PBF]