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  • © 2007

Polynomial Representations of GL_n

with an Appendix on Schensted Correspondence and Littelmann Paths

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-IX
  2. Introduction

    Pages 1-10
  3. The modules Dλ,K

    Pages 33-42
  4. Back Matter

    Pages 72-163

About this book

This second edition of “Polynomial representations of GL (K)” consists of n two parts. The ?rst part is a corrected version of the original text, formatted A in LT X, and retaining the original numbering of sections, equations, etc. E The second is an Appendix, which is largely independent of the ?rst part, but whichleadstoanalgebraL(n,r),de?nedbyP.Littelmann,whichisanalogous to the Schur algebra S(n,r). It is hoped that, in the future, there will be a structure theory of L(n,r) rather like that which underlies the construction of Kac-Moody Lie algebras. We use two operators which act on “words”. The ?rst of these is due to C. Schensted (1961). The second is due to Littelmann, and goes back to a1938paperbyG.deB.Robinsonontherepresentationsofa?nitesymmetric group.Littelmann’soperatorsformthebasisofhiselegantandpowerful“path model” of the representation theory of classical groups. In our Appendix we use Littelmann’s theory only in its simplest case, i.e. for GL . n Essential to my plan was to establish two basic facts connecting the op- ations of Schensted and Littelmann. To these “facts”, or rather conjectures, I gave the names Theorem A and Proposition B. Many examples suggested that these conjectures are true, and not particularly deep. But I could not prove either of them.

Keywords

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

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)."

Authors and Affiliations

  • Department of Mathematics, University of Wales Swansea, Singleton Park, UK

    Manfred Schocker

  • Mathematical Institute, University of Oxford, OX1 3LB, UK

    Karin Erdmann

Bibliographic Information

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions