Polynomial Representations of GL_n: with an Appendix on Schensted Correspondence and Littelmann Paths (Lecture Notes in Mathematics Book 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. 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.

The new corrected and expanded edition adds a special appendix on Schensted Correspondence and Littelmann Paths. This appendix can be read independently of the rest of the volume and is an account of the Littelmann path model for the case gln. The appendix also offers complete proofs of classical theorems of Schensted and Knuth.

Front Matter....Pages I-IX Introduction....Pages 1-10 Polynomial Representations of GL n ( K ): The Schur algebra....Pages 11-22 Weights and Characters....Pages 23-31 The modules D λ,K ....Pages 33-42 The Carter-Lusztig modules V λ,K ....Pages 43-52 Representation theory of the symmetric group....Pages 53-70 Back Matter....Pages 72-163