Linear and projective representations of symmetric groups / Alexander Kleshchev.

By: Kleshchëv, A. S. (Aleksandr Sergeevich)Material type: Text

TextSeries: Cambridge tracts in mathematics ; 163.Publication details: Cambridge : Cambridge University Press, 2005. Description: 1 online resource (xiv, 277 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 0511125747; 9780511125744; 9780511542800; 0511542801Subject(s): Linear algebraic groups | Representations of groups | Algebras, Linear | Geometry, Projective | Symmetry groups | MATHEMATICS -- Group Theory | MATHEMATICS -- Algebra -- Linear | Representations of groups | Algebras, Linear | Geometry, Projective | Symmetry groups | Linear algebraic groups | Algebras, Linear | Geometry, Projective | Linear algebraic groups | Representations of groups | Symmetry groups | Symmetrische Gruppe | Darstellung MathematikGenre/Form: Electronic books. Additional physical formats: Print version:: Linear and projective representations of symmetric groups.DDC classification: 512.5 | 512.2 LOC classification: QA171 | .K54 2005ebOther classification: O152. 6 | O187. 2 Online resources: Click here to access online

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.

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.

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Includes bibliographical references and index.

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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.