- Paperback: 272 pages
- Publisher: Cambridge University Press; 1 edition (Dec 28 1996)
- Language: English
- ISBN-10: 0521567246
- ISBN-13: 978-0521567244
- Product Dimensions: 22.9 x 15.3 x 1.7 cm
- Shipping Weight: 440 g
- Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
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Amazon Bestsellers Rank:
#271,621 in Books (See Top 100 in Books)
- #33 in Books > Science > Mathematics > Pure Mathematics > Group Theory
- #53 in Books > Science > Mathematics > Pure Mathematics > Combinatorics
- See Complete Table of Contents
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Product Details |
Product Description
Product Description
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.
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.
Inside This Book
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First Sentence
The first algorithm, called row-insertion or row bumping, takes a tableau T, and a positive integer x, and constructs a new tableau, donated T x. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
The first algorithm, called row-insertion or row bumping, takes a tableau T, and a positive integer x, and constructs a new tableau, donated T x. Read the first page
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Concordance
Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Most helpful customer reviews
5.0 out of 5 stars
A Fine Synthesis of Combinatorics, Geometry, and Algebra,
By Peter M. Magyar "peter-the-math-geek" (East Lansing, MI United States) - See all my reviews (REAL NAME)
This review is from: Young Tableaux: With Applications to Representation Theory and Geometry (Paperback)
With his usual lucidity, Fulton brings together the surprisingly wide area of mathematics concerned with Young tableaux. These are combinatorial patterns which index basis vectors of group representations (either of the symmetric group or the general linear group). These vectors can be seen as Plucker coordinate functions on non-linear representations, namely homogeneous spaces (Grassmannians and flag varieties). Thus, Young tableaux form an invaluable tool to examine these representations and varieties in concrete detail. Fulton also gives a good exposition of the combinatorial operations on tableaux which reflect the crystal basis structure from quantum GL(n), though Fulton does not explicitly discuss quantum groups. Other good expositions of these topics, from a more algebraic and combinatorial point of view, are Sagan's newly revised "The Symmetric Group", and Stanley's "Enumerative Combinatorics", Vol 2.
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Most Helpful Customer Reviews on Amazon.com (beta) Amazon.com:
5.0 out of 5 stars (1 customer review) 12 of 12 people found the following review helpful
5.0 out of 5 stars
A Fine Synthesis of Combinatorics, Geometry, and Algebra,
By Peter M. Magyar "peter-the-math-geek" - Published on Amazon.com
This review is from: Young Tableaux: With Applications to Representation Theory and Geometry (Paperback)
With his usual lucidity, Fulton brings together the surprisingly wide area of mathematics concerned with Young tableaux. These are combinatorial patterns which index basis vectors of group representations (either of the symmetric group or the general linear group). These vectors can be seen as Plucker coordinate functions on non-linear representations, namely homogeneous spaces (Grassmannians and flag varieties). Thus, Young tableaux form an invaluable tool to examine these representations and varieties in concrete detail. Fulton also gives a good exposition of the combinatorial operations on tableaux which reflect the crystal basis structure from quantum GL(n), though Fulton does not explicitly discuss quantum groups. Other good expositions of these topics, from a more algebraic and combinatorial point of view, are Sagan's newly revised "The Symmetric Group", and Stanley's "Enumerative Combinatorics", Vol 2.
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