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Young Tableaux

Young Tableaux
With Applications to Representation Theory and Geometry

$52.99 (P)

Part of London Mathematical Society Student Texts

  • Date Published: December 1996
  • availability: Available
  • format: Paperback
  • isbn: 9780521567244

$ 52.99 (P)
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  • This book develops the combinatorics of Young tableaux and shows them in action in the algebra of symmetric functions, representations of the symmetric and general linear groups, and the geometry of flag varieties. The first part of the book is a self-contained presentation of the basic combinatorics of Young tableaux, including the remarkable constructions of "bumping" and "sliding", and several interesting correspondences. In Part II the author uses these results to study representations with geometry on Grassmannians and flag manifolds, including their Schubert subvarieties, and the related Schubert polynomials. Much of this material has never before appeared in book form. There are numerous exercises throughout, with hints and answers provided. Researchers in representation theory and algebraic geometry as well as in combinatorics will find this book interesting and useful, while students will find the intuitive presentation easy to follow.

    • Shows relations among combinatorics, algebraic geometry, representation theory
    • Written in the style of lectures, with many illustrations and examples and exercises
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    Product details

    • Date Published: December 1996
    • format: Paperback
    • isbn: 9780521567244
    • length: 272 pages
    • dimensions: 229 x 153 x 17 mm
    • weight: 0.369kg
    • availability: Available
  • Table of Contents

    Part I. Calculus Of Tableux:
    1. Bumping and sliding
    2. Words: the plactic monoid
    3. Increasing sequences: proofs of the claims
    4. The Robinson-Schensted-Knuth Correspondence
    5. The Littlewood-Richardson rule
    6. Symmetric polynomials
    Part II. Representation Theory:
    7. Representations of the symmetric group
    8. Representations of the general linear group
    Part III. Geometry:
    9. Flag varieties
    10. Schubert varieties and polynomials
    Appendix A
    Appendix B.

  • Author

    William Fulton, University of Chicago

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