Linear and projective representations of symmetric groups / Alexander Kleshchev.

Format:

Book

Author/Creator:

Kleshchëv, A. S. (Aleksandr Sergeevich), author.

Series:

Cambridge tracts in mathematics ; 163.

Cambridge tracts in mathematics ; 163

Language:

English

Subjects (All):

Symmetry groups.

Representations of groups.

Modular representations of groups.

Hecke algebras.

Superalgebras.

Linear algebraic groups.

Algebras, Linear.

Geometry, Projective.

Physical Description:

1 online resource (xiv, 277 pages) : digital, PDF file(s).

Other Title:

Linear & Projective Representations of Symmetric Groups

Place of Publication:

Cambridge : Cambridge University Press, 2005.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-13981-3

9786611836696

1-281-83669-9

0-511-18137-X

9786610415755

0-511-12574-7

0-511-19807-8

0-511-33131-2

0-511-54280-1

0-511-12488-0

OCLC:

171137257