Format:
1 Online-Ressource (xiv, 277 pages)
,
digital, PDF file(s).
ISBN:
9780511542800
Series Statement:
Cambridge tracts in mathematics 163
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
,
1. Notation and generalities -- 2. Symmetric groups I -- 3. Degenerate affine Hecke algebra -- 4. First results on H[subscript n]-modules -- 5. Crystal operators -- 6. Character calculations -- 7. Integral representations and cyclotomic Hecke algebras -- 8. Functors e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] -- 9. Construction of U[subscript z][superscript +] and irreducible modules -- 10. Identification of the crystal -- 11. Symmetric groups II -- 12. Generalities on superalgebra -- 13. Sergeev superalgebras -- 14. Affine Sergeev superalgebras -- 15. Integral representations and cyclotomic Sergeev algebras -- 16. First results on X[subscript n]-modules -- 17. Crystal operators for X[subscript n] -- 18. Character calculations for X[subscript n] -- 19. Operators e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] -- 20. Construction of U[subscript z][superscript +] and irreducible modules -- 21. Identification of the crystal -- 22. Double covers.
Additional Edition:
ISBN 9781107471641
Additional Edition:
ISBN 9780521837033
Additional Edition:
ISBN 9780521837033
Additional Edition:
ISBN 9781107471641
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9780521837033
Language:
English
DOI:
10.1017/CBO9780511542800
