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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.

By: Contributor(s): Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 830.Publication details: Berlin ; New York : Springer, ©2007.Edition: 2nd corr. and augm. edDescription: 1 online resource (ix, 161 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540469599
  • 3540469591
  • 3540469443
  • 9783540469445
  • 6610745765
  • 9786610745760
Other title:
  • Polynomial representations of GLn
Contained works:
  • Erdmann, Karin, 1948- Schensted correspondence and Littelmann paths
Subject(s): Additional physical formats: Print version:: Polynomial representations of GL[subscript n].DDC classification:
  • 512.5 22
LOC classification:
  • QA174.7.S96 G74 2006
Other classification:
  • O174. 14
Online resources:
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.
In: OhioLINK electronic book center In: SpringerLinkSummary: 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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Includes bibliographical references (pages 155-157) and index.

Print version record.

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.

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.

Available to OhioLINK libraries.

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