Polynomial Representations of GL n / by James A. Green, Manfred Schocker, Karin Erdmann.

Format:

Book

Author/Creator:

Green, James A., author.

Schocker, Manfred, author.

Erdmann, Karin, 1948- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 830.

Lecture Notes in Mathematics, 0075-8434 ; 830

Language:

English

Subjects (All):

Group theory.

Algebra.

Combinatorial analysis.

Mathematics.

Group Theory and Generalizations.

Associative Rings and Algebras.

Non-associative Rings and Algebras.

Combinatorics.

Real Functions.

Local Subjects:

Group Theory and Generalizations.

Associative Rings and Algebras.

Non-associative Rings and Algebras.

Combinatorics.

Real Functions.

Physical Description:

1 online resource (X, 166 pages).

Edition:

Second corrected and augmented edition.

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.

System Details:

text file PDF

Summary:

The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, 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 gln. 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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9783540469599

Access Restriction:

Restricted for use by site license.