Title Polynomial representations of GL[subscript n] / J.A. Green ; with an appendix on Schensted correspondence and Littelmann paths by K. Erdmann, J.A. Green, and M. Schocker

Edition 2nd corr. and augm. ed Published Berlin ; New York : Springer, ©2007

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Description 1 online resource (ix, 161 pages) : illustrations Series Lecture notes in mathematics, 0075-8434 ; 830 Lecture notes in mathematics (Springer-Verlag) ; 830. Contents 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 Summary 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 Bibliography Includes bibliographical references (pages 155-157) and index Notes Print version record In OhioLINK electronic book center SpringerLink Subject Linear algebraic groups. Symmetry groups. Representations of groups. MATHEMATICS -- Algebra -- Linear. Symmetry groups. Representations of groups. Groupes abéliens. Semi-groupes. Représentations de groupes. Théorie des groupes. Mathématiques. Linear algebraic groups. Linear algebraic groups Representations of groups Symmetry groups Form Electronic book Author Schocker, Manfred Erdmann, Karin, 1948- Schensted correspondence and Littelmann paths ISBN 9783540469599 3540469591 3540469443 9783540469445 6610745765 9786610745760

Other Titles Polynomial representations of GLn Schensted correspondence and Littelmann paths Schensted correspondence and Littelmann paths Schensted correspondence and Littelmann paths Schensted correspondence and Littelmann paths Schensted correspondence and Littelmann paths

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