James A. Green

Polynomial Representations of GL_n (eBook, PDF)

with an Appendix on Schensted Correspondence and Littelmann Paths

• Format: PDF

Produktbeschreibung

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 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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 166
• Erscheinungstermin: 15. November 2006
• Englisch
• ISBN-13: 9783540469599
• Artikelnr.: 44130052

Autorenporträt

J. A. Green, University of Oxford, UK

Inhaltsangabe

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.

Rezensionen

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)."