Young Tableaux: With Applications to Representation Theory and Geometry

Front Cover
Cambridge University Press, 1997 - Mathematics - 260 pages
Young tableaux are fillings of the boxes of diagrams that correspond to partitions with positive integers, that are strictly increasing down columns and weakly increasing along rows. The aim of this book is to develop the combinatorics of Young tableaux and to show them in action in the algebra of symmetric functions, the representations of the symmetric and general linear groups, and the geometry of flag varieties. Many of these applications have not been available in book form.
 

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Contents

Preface page
8
Bumping and sliding
8
Words the plactic monoid
17
Increasing sequences proofs of the claims
30
The RobinsonSchenstedKnuth correspondence
36
The LittlewoodRichardson rule
58
Symmetric polynomials
72
Representations of the symmetric group
83
Representations of the general linear group
104
Flag varieties
131
Schubert varieties and polynomials
154
Appendix A Combinatorial variations
183
Appendix B On the topology of algebraic varieties
211
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