Green Polynomial Representations of GL_n

with an Appendix on Schensted Correspondence and Littelmann Paths
Erscheinungsjahr 2008
ISBN: 978-3-540-38379-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 830, 120 Seiten, eBook

Reihe: Lecture Notes in Mathematics

The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GL n . This classic account of matrix representations, the Schur algebra, the modular representations of GL n , 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 gl n . In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the representation 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.

Zielgruppe

Research

Autoren/Hrsg.

Green, James A.

Weitere Mitwirkende

Erdmann, K.

Green, James A.

Schocker, Manfred

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.