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  3. Character Theory and the McKay Conjecture
  • Cited by 61
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2018
      April 2018
      ISBN:
      9781108552790
      9781108428446
      DOI:
      https://doi.org/10.1017/9781108552790
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.47kg, 250 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Algebra
      Series:
      Cambridge Studies in Advanced Mathematics (175)
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    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    Cambridge Studies in Advanced Mathematics (175)
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    Book description

    The McKay conjecture is the origin of the counting conjectures in the representation theory of finite groups. This book gives a comprehensive introduction to these conjectures, while assuming minimal background knowledge. Character theory is explored in detail along the way, from the very basics to the state of the art. This includes not only older theorems, but some brand new ones too. New, elegant proofs bring the reader up to date on progress in the field, leading to the final proof that if all finite simple groups satisfy the inductive McKay condition, then the McKay conjecture is true. Open questions are presented throughout the book, and each chapter ends with a list of problems, with varying degrees of difficulty.

    Reviews

    'Navarro continues his informative preface with an exhaustive overview of the work done on this conjecture, and he includes a number of fascinating insights and elaborations.'

    Michael Berg Source: MAA Reviews

    ‘… the author has done an excellent job in presenting a road leading from the basics to the present frontiers in representation theory.’

    Burkhard Külshammer Source: zbMATH

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