© 1980
Polynomial Representations of GL_{n}
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Part of the Lecture Notes in Mathematics book series (LNM, volume 830)
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© 1980
Part of the Lecture Notes in Mathematics book series (LNM, volume 830)
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.