Character Theory and the McKay Conjecture

Nonfiction, Science & Nature, Mathematics, Algebra
Cover of the book Character Theory and the McKay Conjecture by Gabriel Navarro, Cambridge University Press
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Author: Gabriel Navarro ISBN: 9781108631723
Publisher: Cambridge University Press Publication: April 26, 2018
Imprint: Cambridge University Press Language: English
Author: Gabriel Navarro
ISBN: 9781108631723
Publisher: Cambridge University Press
Publication: April 26, 2018
Imprint: Cambridge University Press
Language: English

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.

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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.

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