Polynomial Representations of GL_n

with an Appendix on Schensted Correspondence and Littelmann Paths
2. corr. and augmented Auflage 2007
ISBN: 978-3-540-46944-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 830, 166 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 283 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Green, James A.

Weitere Mitwirkende

Erdmann, K.

Green, James A.

Schocker, Manfred

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

Preface to the second edition.- J. A. Green: Polynomial representations of GLn: 1.Introduction.- 2.Polynomial representations of GL_n(K): The Schur algebra.- 3.Weights and characters.- 4.The module D_{\lambda, K}.- 5.The Carter-Lusztig modules V_{\lambda, K}.- 6.Representation theory of the symmetric group.- Appendix on Schensted correspondence and Littelmann paths by K. Erdmann, J. A. Green and M. Schocker: A. Introduction.- B. The Schensted process.- C. Schensted and Littelmann.- D. Theorem A and some of its consequences.- E. Tables.- Index of Symbols.- References.- Index.