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.

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)."

Bibliographic Information

Book Title: Polynomial Representations of GL_n
Book Subtitle: with an Appendix on Schensted Correspondence and Littelmann Paths
Authors: James A. Green
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0092296
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1980
eBook ISBN: 978-3-540-38379-6Published: 15 July 2008
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 120
Topics: Real Functions

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Polynomial Representations of GL_n

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Table of contents (6 chapters)

Front Matter

Introduction