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

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9783540469445: Polynomial Representations of GL_n: with an Appendix on Schensted Correspondence and Littelmann Paths (Lecture Notes in Mathematics)
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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.

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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.

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From the reviews: LNM 830 "is now regarded as the standard text on the finite-dimensional polynomial representations of the general linear group GL_n(K)."

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