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Linear and Projective Representations of Symmetric Groups


Part of Cambridge Tracts in Mathematics

  • Date Published: March 2009
  • availability: Available
  • format: Paperback
  • isbn: 9780521104180

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About the Authors
  • 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.

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    Product details

    • Date Published: March 2009
    • format: Paperback
    • isbn: 9780521104180
    • length: 292 pages
    • dimensions: 229 x 152 x 17 mm
    • weight: 0.43kg
    • availability: Available
  • Table of Contents

    Part I. Linear Representations:
    1. Notion and generalities
    2. Symmetric groups I
    3. Degenerate affine Hecke algebra
    4. First results on Hn modules
    5. Crystal operators
    6. Character calculations
    7. Integral representations and cyclotomic Hecke algebras
    8. Functors e and f
    9. Construction of Uz and irreducible modules
    10. Identification of the crystal
    11. Symmetric groups II
    Part II. Projective Representations:
    12. Generalities on superalgebra
    13. Sergeev superalgebras
    14. Affine Sergeev superalgebras
    15. Integral representations and cyclotomic Sergeev algebras
    16. First results on Xn modules
    17. Crystal operators fro Xn
    18. Character calculations for Xn
    19. Operators e and f
    20. Construction of Uz and irreducible modules
    21. Identification of the crystal
    22. Double covers

  • Author

    Alexander Kleshchev, University of Oregon
    Alexander Kleshchev is a Professor of Mathematics at the University of Oregon.

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