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E-book
Author Kleshchëv, A. S. (Aleksandr Sergeevich)

Title Linear and projective representations of symmetric groups / Alexander Kleshchev
Published Cambridge : Cambridge University Press, 2005

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Description 1 online resource (xiv, 277 pages) : illustrations
Series Cambridge tracts in mathematics ; 163
Cambridge tracts in mathematics ; 163.
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
Bibliography Includes bibliographical references and index
Notes Print version record
Subject 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 Mathematik
Form Electronic book
ISBN 0511125747
9780511125744
9780511542800
0511542801