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At the crossroads of representation theory, algebraic geometry and finite group theory, this 2004 book blends together many of the main concerns of modern algebra, with full proofs of some of the most remarkable achievements in the area. Cabanes and Enguehard follow three main themes: first, applications of étale cohomology, leading to the proof of the recent Bonnafé-Rouquier theorems. The second is a straightforward and simplified account of the Dipper-James theorems relating irreducible characters and modular representations. The final theme is local representation theory. One of the main results here is the authors' version of Fong-Srinivasan theorems. Throughout the text is illustrated by many examples and background is provided by several introductory chapters on basic results and appendices on algebraic geometry and derived categories. The result is an essential introduction for graduate students and reference for all algebraists.

Finite groups. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Groups, Finite --- Modules (Algebra)

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Representations of Lie groups --- Representations of Lie algebras --- Lie algebras. --- Lie groups. --- Representations of Lie algebras. --- Representations of Lie groups. --- 512.8 --- 512.81 --- 512.81 Lie groups --- Lie groups --- Lie groups, Lie algebras --- Representations of algebras --- Lie algebras --- Groups, Lie --- Symmetric spaces --- Topological groups --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Representations of groups --- Representations of algebras. --- Representations of groups.

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This book is based on a one-semester course for advanced undergraduates specializing in physical chemistry. I am aware that the mathematical training of most science majors is more heavily weighted towards analysis – typ- ally calculus and differential equations – than towards algebra. But it remains my conviction that the basic ideas and applications of group theory are not only vital, but not dif?cult to learn, even though a formal mathematical setting with emphasis on rigor and completeness is not the place where most chemists would feel most comfortable in learning them. The presentation here is short, and limited to those aspects of symmetry and group theory that are directly useful in interpreting molecular structure and spectroscopy. Nevertheless I hope that the reader will begin to sense some of the beauty of the subject. Symmetry is at the heart of our understanding of the physical laws of nature. If a reader is happy with what appears in this book, I must count this a success. But if the book motivates a reader to move deeper into the subject, I shall be grati?ed.

Symmetry groups. --- Quantum chemistry. --- Chemistry, Physical organic. --- Physical Chemistry. --- Atomic, Molecular, Optical and Plasma Physics. --- Physical chemistry. --- Atoms. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Chemistry, Physical and theoretical --- Matter --- Stereochemistry --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Chemistry --- Constitution --- Chemistry, Quantum --- Quantum theory --- Excited state chemistry --- Groups, Symmetry --- Symmetric groups --- Crystallography, Mathematical --- Representations of groups