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Young Tableaux: With Applications to Representation Theory and Geometry

โœ Scribed by William Fulton


Publisher
Cambridge University Press
Year
1999
Tongue
English
Leaves
270
Series
London Mathematical Society Student Texts #35
Category
Library

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โœฆ Table of Contents


Title page
Contents
Preface
Notation
Part I: Calculus of tableaux
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
Appendices
A. Combinatorial variations
B. On the topology of algebraic varieties
Answers and References
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Appendix A
Appendix B
Bibliography
Index of Notation
General Index


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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 combinatoric