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  • Book
  • © 1980

Polynomial Representations of GL_n

with an Appendix on Schensted Correspondence and Littelmann Paths

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 830)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-VI
  2. Introduction

    • James A. Green
    Pages 1-17
  3. Weights and characters

    • James A. Green
    Pages 36-49
  4. The modules Dλ,K

    • James A. Green
    Pages 50-64
  5. The Carter-Lusztig modules Vλ,K

    • James A. Green
    Pages 65-79
  6. Representation theory of the symmetric group

    • James A. Green
    Pages 80-112
  7. Back Matter

    Pages 113-118

About this book

The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory.

The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the representation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self-contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.

Keywords

  • Combinatorics
  • DEX
  • Matrix
  • Schur algebra
  • Young tableaux
  • algebra
  • boundary element method
  • combinatorics on words
  • model
  • polynomial representation of the general linear group
  • presentation
  • proof
  • representation of the symmetric group
  • representation theory
  • theorem

Reviews

From the reviews: LNM 830 "is now regarded as the standard text on the finite-dimensional polynomial representations of the general linear group GL_n(K)."

Bibliographic Information

  • Book Title: Polynomial Representations of GL_n

  • Book Subtitle: with an Appendix on Schensted Correspondence and Littelmann Paths

  • Authors: James A. Green

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0092296

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1980

  • eBook ISBN: 978-3-540-38379-6Published: 15 July 2008

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 120

  • Topics: Real Functions

Buying options

eBook USD 74.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions