Young Tableaux
Young Tableaux
$58.99
USDThis 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
Product details
December 1996Paperback
9780521567244
272 pages
229 × 153 × 17 mm
0.369kg
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.
