The Character Theory of Finite Groups of Lie Type

The Character Theory of Finite Groups of Lie Type
Author: Meinolf Geck
Publisher: Cambridge University Press
Total Pages: 406
Release: 2020-02-27
Genre: Mathematics
ISBN: 1108808905

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.

Representations of Finite Groups of Lie Type

Representations of Finite Groups of Lie Type
Author: François Digne
Publisher: Cambridge University Press
Total Pages: 267
Release: 2020-03-05
Genre: Mathematics
ISBN: 1108481485

An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris.

Linear Algebraic Groups and Finite Groups of Lie Type

Linear Algebraic Groups and Finite Groups of Lie Type
Author: Gunter Malle
Publisher: Cambridge University Press
Total Pages: 324
Release: 2011-09-08
Genre: Mathematics
ISBN: 113949953X

Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.

Finite Groups of Lie Type

Finite Groups of Lie Type
Author: Roger W. Carter
Publisher:
Total Pages: 570
Release: 1993-08-24
Genre: Mathematics
ISBN:

The finite groups of Lie type are of basic importance in the theory of groups. A classic in its field, this book presents the theories of finite groups of Lie type in a clear and accessible style, especially with regard to the main concepts of the theory and the techniques of proof used, and gives a detailed exposition of the complex representation theory.

Representation Theory of Finite Groups: a Guidebook

Representation Theory of Finite Groups: a Guidebook
Author: David A. Craven
Publisher: Springer Nature
Total Pages: 297
Release: 2019-08-30
Genre: Mathematics
ISBN: 3030217922

This book provides an accessible introduction to the state of the art of representation theory of finite groups. Starting from a basic level that is summarized at the start, the book proceeds to cover topics of current research interest, including open problems and conjectures. The central themes of the book are block theory and module theory of group representations, which are comprehensively surveyed with a full bibliography. The individual chapters cover a range of topics within the subject, from blocks with cyclic defect groups to representations of symmetric groups. Assuming only modest background knowledge at the level of a first graduate course in algebra, this guidebook, intended for students taking first steps in the field, will also provide a reference for more experienced researchers. Although no proofs are included, end-of-chapter exercises make it suitable for student seminars.

A Course in Finite Group Representation Theory

A Course in Finite Group Representation Theory
Author: Peter Webb
Publisher: Cambridge University Press
Total Pages: 339
Release: 2016-08-19
Genre: Mathematics
ISBN: 1107162394

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Lie Algebras of Finite and Affine Type

Lie Algebras of Finite and Affine Type
Author: Roger William Carter
Publisher: Cambridge University Press
Total Pages: 662
Release: 2005-10-27
Genre: Mathematics
ISBN: 9780521851381

This book provides a thorough but relaxed mathematical treatment of Lie algebras.

Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras

Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras
Author: Meinolf Geck
Publisher: Oxford University Press
Total Pages: 478
Release: 2000
Genre: Mathematics
ISBN: 9780198502500

Finite Coxeter groups and related structures arise naturally in several branches of mathematics such as the theory of Lie algebras and algebraic groups. The corresponding Iwahori-Hecke algebras are then obtained by a certain deformation process which have applications in the representation theory of groups of Lie type and the theory of knots and links. This book develops the theory of conjugacy classes and irreducible character, both for finite Coxeter groups and the associated Iwahori-Hecke algebras. Topics covered range from classical results to more recent developments and are clear and concise. This is the first book to develop these subjects both from a theoretical and an algorithmic point of view in a systematic way, covering all types of finite Coxeter groups.

The Character Theory of Finite Groups of Lie Type

The Character Theory of Finite Groups of Lie Type
Author: Meinolf Geck
Publisher: Cambridge University Press
Total Pages: 405
Release: 2020-02-27
Genre: Mathematics
ISBN: 1108489621

A comprehensive guide to the vast literature and range of results around Lusztig's character theory of finite groups of Lie type.