Polynomial Representations of GL_n: with an Appendix on Schensted Correspondence and Littelmann Paths by Karin ErdmannPolynomial Representations of GL_n: with an Appendix on Schensted Correspondence and Littelmann Paths by Karin Erdmann

Polynomial Representations of GL_n: with an Appendix on Schensted Correspondence and Littelmann…

byKarin Erdmann, James A. Green, Manfred Schocker

Paperback | November 30, 2006

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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.
Title:Polynomial Representations of GL_n: with an Appendix on Schensted Correspondence and Littelmann…Format:PaperbackDimensions:166 pagesPublished:November 30, 2006Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540469443

ISBN - 13:9783540469445

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Table of Contents

Polynomial Representations of GLn(K): The Schur algebra.- Weights and Characters.- The modules D?,K.- The Carter-Lusztig modules V?,K.- Representation theory of the symmetric group.

Editorial 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)."