© 1980

Polynomial Representations of GLn

  • Authors

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

Table of contents

  1. Front Matter
    Pages I-VI
  2. James A. Green
    Pages 1-17
  3. James A. Green
    Pages 36-49
  4. James A. Green
    Pages 50-64
  5. James A. Green
    Pages 65-79
  6. 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 repesentation 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.


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

Bibliographic information

  • Book Title Polynomial Representations of GLn
  • Authors James A. Green
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1980
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-10258-8
  • eBook ISBN 978-3-540-38379-6
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages VIII, 120
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Real Functions
  • Buy this book on publisher's site


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)."