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The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. As a text, this book contains ample material for a one semester course. Exercises are provided at the end of most sections; the results of some are used later in the text. Representation theory is applied in number theory, combinatorics and in many areas of algebra. This book will serve as an excellent introduction to those interested in the subject itself or its applications.

Finite groups. --- Modular representations of groups.

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Group theory --- Modular representations of groups. --- Finite groups. --- MODULAR REPRESENTATIONS of groups --- Finite groups --- Modular representations of groups --- #KOPO:Prof. R. Holvoet --- Representations of groups --- Groups, Finite --- Modules (Algebra) --- Groupes finis --- Representation

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Kazhdan-Lusztig polynomials --- Modular representations of groups --- Semisimple Lie groups --- Verma modules

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Group theory --- 512 --- Finite groups --- Modular representations of groups --- Representations of groups --- Groups, Finite --- Modules (Algebra) --- Algebra --- 512 Algebra --- Groupes finis --- Représentations de groupes --- Groupes (algebre)

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Finite groups of Lie type encompass most of the finite simple groups. Their representations and characters have been studied intensively for half a century, though some key problems remain unsolved. This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic. As a subtheme, the relationship between ordinary and modular representations is explored, in the context of Deligne-Lusztig characters. One goal has been to make the subject more accessible to those working in neighbouring parts of group theory, number theory, and topology. Core material is treated in detail, but the later chapters emphasize informal exposition accompanied by examples and precise references.

Lie groups. --- Modular representations of groups. --- Finite simple groups. --- Simple groups, Finite --- Finite groups --- Linear algebraic groups --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Representations of Lie groups. --- Lie groups --- Representations of groups