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  3. Representation Theory
  • Cited by 16
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    • Publisher:
      Cambridge University Press
      Publication date:
      December 2014
      February 2015
      ISBN:
      9781139976824
      9781107082052
      DOI:
      https://doi.org/10.1017/CBO9781139976824
      Dimensions:
      (244 x 170 mm)
      Weight & Pages:
      0.46kg, 202 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
      Series:
      Cambridge Studies in Advanced Mathematics (147)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
    Series:
    Cambridge Studies in Advanced Mathematics (147)
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    Book description

    This book discusses the representation theory of symmetric groups, the theory of symmetric functions and the polynomial representation theory of general linear groups. The first chapter provides a detailed account of necessary representation-theoretic background. An important highlight of this book is an innovative treatment of the Robinson–Schensted–Knuth correspondence and its dual by extending Viennot's geometric ideas. Another unique feature is an exposition of the relationship between these correspondences, the representation theory of symmetric groups and alternating groups and the theory of symmetric functions. Schur algebras are introduced very naturally as algebras of distributions on general linear groups. The treatment of Schur–Weyl duality reveals the directness and simplicity of Schur's original treatment of the subject. In addition, each exercise is assigned a difficulty level to test readers' learning. Solutions and hints to most of the exercises are provided at the end.

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