Description
CAMBRIDGE UNIVERSITY PRESS Linear And Projective Representations Of Symmetric Groups (Hb 2005) by KLESHCHEV A
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.