Character Theory and the McKay Conjecture

by Gabriel Navarro

Overview

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.

Product Details

ISBN-13:	9781108428446
Publisher:	Cambridge University Press
Publication date:	04/26/2018
Series:	Cambridge Studies in Advanced Mathematics , #175
Pages:	250
Product dimensions:	6.14(w) x 9.25(h) x 0.71(d)

About the Author

Gabriel Navarro is Professor in the Department of Mathematics at the University of Valencia. He has published over 160 papers, and the widely-cited volume Characters and Blocks of Finite Groups (Cambridge, 1998). He is a leading researcher in character theory and the McKay conjecture.

Table of Contents

Preface; Notation; 1. The basics; 2. Action on characters by automorphisms; 3. Galois action on characters; 4. Character values and identities; 5. Characters over a normal subgroup; 6. Extension of characters; 7. Degrees of characters; 8. The Howlett–Isaacs theorem; 9. Global-local counting conjectures; 10. A reduction theorem for the McKay conjecture; Appendix; Bibliographic notes; References; Index.

Editorial 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, 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, zbMATH

From the Publisher