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LMSST: 35 Young Tableaux: With Applications to Representation Theory and Geometry
Author(s): Fulton (Author)
- Publisher: Cambridge University Press
- Publication Date: 12 Jan. 2008
- Language: English
- Print length: 272 pages
- ISBN-10: 0521567246
- ISBN-13: 9780521567244
Book 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.
Editorial Reviews
Book Description
Describes combinatorics involving Young tableaux and their uses in representation theory and algebraic geometry.
From the Back Cover
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.
