| Description |
1 online resource (xiv, 277 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Cambridge tracts in mathematics ; 163
|
|
Cambridge tracts in mathematics ; 163.
|
| Bibliography |
Includes bibliographical references and index. |
| 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 combinatorics, Lie theory, and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski, Brundan, and the author. Much of this work has only appeared in the research literature before. However, to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract. |
| 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. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Linear algebraic groups.
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Linear algebraic groups. |
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Representations of groups.
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Representations of groups. |
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Algebras, Linear.
|
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Algebras, Linear. |
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Geometry, Projective.
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Geometry, Projective. |
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Symmetry groups.
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Symmetry groups. |
| Genre/Form |
Electronic books.
|
| Other Form: |
Print version: Kleshchëv, A.S. (Aleksandr Sergeevich). Linear and projective representations of symmetric groups. Cambridge : Cambridge University Press, 2005 0521837030 (OCoLC)58556088 |
| ISBN |
0511125747 (electronic book) |
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9780511125744 (electronic book) |
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9780511542800 (electronic book) |
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0511542801 (electronic book) |
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0521837030 (Cloth) |
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9780521837033 |
|
