Young Tableaux

With Applications to Representation Theory and Geometry

William Fulton (University of Chicago), J. Bruce

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English

Cambridge University Press
26 May 1997

Mathematics & Sciences; Combinatorics & graph theory

Series: London Mathematical Society Student Texts

"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."

By: William Fulton (University of Chicago)
Series edited by: J. Bruce
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 35
Dimensions: Height: 229mm, Width: 153mm, Spine: 17mm
Weight: 369g
ISBN: 9780521567244
ISBN 10: 0521567246
Series: London Mathematical Society Student Texts
Pages: 272
Publication Date: 26 May 1997
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.