The Character Theory of Finite Groups of Lie Type: A Guided Tour

Meinolf Geck; Gunter Malle

doi:10.1017/9781108779081

The Character Theory of Finite Groups of Lie Type

A Guided Tour

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Rizo, Noelia Schaeffer Fry, A.A. and Vallejo, Carolina 2021. Principal blocks with 5 irreducible characters. Journal of Algebra, Vol. 585, Issue. , p. 316.

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Meinolf Geck, Universität Stuttgart, Gunter Malle, Technische Universität Kaiserslautern, Germany

Publisher:: Cambridge University Press
Online publication date:: February 2020
Print publication year:: 2020
Online ISBN:: 9781108779081
DOI:: https://doi.org/10.1017/9781108779081

Subjects:: Mathematics (general), Mathematics, Algebra
Series:: Cambridge Studies in Advanced Mathematics (187)

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The Character Theory of Finite Groups of Lie Type
Meinolf Geck, Gunter Malle
Online ISBN: 9781108779081

Book DOI: https://doi.org/10.1017/9781108779081
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Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods from algebraic geometry, topology, combinatorics and computer algebra, and has since evolved substantially. With this book, the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne–Michel. Focusing on applications in finite group theory, the authors gather previously scattered results and allow the reader to get to grips with the large body of literature available on the subject, covering topics such as regular embeddings, the Jordan decomposition of characters, d-Harish–Chandra theory and Lusztig induction for unipotent characters. Requiring only a modest background in algebraic geometry, this useful reference is suitable for beginning graduate students as well as researchers.

‘The book is very well written … the entire text is meticulously referenced and succeeds in giving a fascinating guided tour through this vast territory.’

Donald L. White Source: Mathematical Reviews

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The Character Theory of Finite Groups of Lie Type

A Guided Tour

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-x

1 - Reductive Groups and Steinberg Maps
pp 1-91

2 - Lusztig’s Classification of Irreducible Characters
pp 92-210

3 - Harish-Chandra Theories
pp 211-270

4 - Unipotent Characters
pp 271-362

Appendix - Further Reading and Open Questions
pp 363-370

References
pp 371-389

Index
pp 390-394

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The Character Theory of Finite Groups of Lie Type

A Guided Tour

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