TY  - BOOK
AU  - Green,James A.
AU  - Schocker,Manfred
AU  - Erdmann,Karin
ED  - SpringerLink (Online service)
TI  - Polynomial Representations of GL n
T2  - Lecture Notes in Mathematics,
SN  - 9783540469599
AV  - QA174-183 
U1  - 512.2 23
PY  - 2007///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Group theory
KW  - Algebra
KW  - Combinatorics
KW  - Mathematics
KW  - Group Theory and Generalizations
KW  - Associative Rings and Algebras
KW  - Non-associative Rings and Algebras
KW  - Real Functions
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/3-540-46944-3
ER  -