Young Tableaux
With Applications to Representation Theory and Geometry
1st Edition
Published on 11. July 2013
978-1-107-10873-8 (ISBN)
Description
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, 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 these results are used 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 appeared in book form.There are numerous exercises throughout, with hints or answers provided. Researchers in representation theory and algebraic geometry as well as in combinatorics will find Young Tableaux interesting and useful; students will find the intuitive presentation easy to follow.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
File size
11903,86 MB
ISBN-13
978-1-107-10873-8 (9781107108738)
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Schweitzer Classification
Other editions
Additional editions
Book
01/1997
Cambridge University Press
€55.71
Article exhausted; check for reprint
Book
12/1996
Cambridge University Press
€67.00
Shipment within 15-20 days
Person
Content
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.
