Ebook: Polynomial Representations of GLn
Author: James A. Green (auth.)
- Tags: Real Functions
- Series: Lecture Notes in Mathematics 830
- Year: 1980
- Publisher: Springer Berlin Heidelberg
- Language: English
- pdf
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.
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.
Content:
Front Matter....Pages -
Introduction....Pages 1-17
Polynomial representations of GLn(K): The Schur algebra....Pages 18-35
Weights and characters....Pages 36-49
The modules D?,K ....Pages 50-64
The Carter-Lusztig modules V?,K ....Pages 65-79
Representation theory of the symmetric group....Pages 80-112
Back Matter....Pages -
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.
Content:
Front Matter....Pages -
Introduction....Pages 1-17
Polynomial representations of GLn(K): The Schur algebra....Pages 18-35
Weights and characters....Pages 36-49
The modules D?,K ....Pages 50-64
The Carter-Lusztig modules V?,K ....Pages 65-79
Representation theory of the symmetric group....Pages 80-112
Back Matter....Pages -
....