Character Theory and the McKay Conjecture

Inbunden, Engelska, 2018

Del 175 i serien Cambridge Studies in Advanced Mathematics

771 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2018-04-26
Mått:156 x 235 x 18 mm
Vikt:470 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Studies in Advanced Mathematics
Antal sidor:250
Förlag:Cambridge University Press
ISBN:9781108428446

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

'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

Innehållsförteckning

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.