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  3. Character Theory and the McKay Conjecture
  • Cited by 59
Publisher:
Cambridge University Press
Online publication date:
May 2018
Print publication year:
2018
Online ISBN:
9781108552790
DOI:
https://doi.org/10.1017/9781108552790
Subjects:
Mathematics (general), Mathematics, Algebra
Series:
Cambridge Studies in Advanced Mathematics (175)
Information

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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