© 2007

Polynomial Representations of GLn


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

Table of contents

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 Representation theory Schur algebra Young tableaux algebra combinatorics on words polynomial representation of the general linear group representation of the symmetric group

Authors and affiliations

  1. 1.Department of MathematicsUniversity of Wales SwanseaSingleton ParkUK
  2. 2.Mathematical InstituteUniversity of OxfordOX1 3LBUK

Bibliographic information


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)."