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Representations of algebraic groups

Group theory --- Representations of groups. --- Linear algebraic groups. --- Representations of groups --- Linear algebraic groups --- Algebraic groups, Linear --- Geometry, Algebraic --- Algebraic varieties --- Group representation (Mathematics) --- Groups, Representation theory of

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51 --- Invariants --- Linear algebraic groups --- Representations of groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Algebraic groups, Linear --- Geometry, Algebraic --- Algebraic varieties --- 51 Mathematics --- Mathematics

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This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.

Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- 512.542 --- 512.542 Finite groups --- Finite groups --- Representations of groups

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Group theory --- Physics --- Representations of groups. --- Symmetry groups. --- Représentations de groupes --- Groupes symétriques --- Representations of groups --- Représentations de groupes --- Groupes symétriques --- Symmetry groups --- Groups, Symmetry --- Symmetric groups --- Crystallography, Mathematical --- Quantum theory --- Group representation (Mathematics) --- Groups, Representation theory of

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The dual space of a locally compact group G consists of the equivalence classes of irreducible unitary representations of G. This book provides a comprehensive guide to the theory of induced representations and explains its use in describing the dual spaces for important classes of groups. It introduces various induction constructions and proves the core theorems on induced representations, including the fundamental imprimitivity theorem of Mackey and Blattner. An extensive introduction to Mackey analysis is applied to compute dual spaces for a wide variety of examples. Fell's contributions to understanding the natural topology on the dual are also presented. In the final two chapters, the theory is applied in a variety of settings including topological Frobenius properties and continuous wavelet transforms. This book will be useful to graduate students seeking to enter the area as well as experts who need the theory of unitary group representations in their research.

Locally compact groups. --- Topological spaces. --- Representations of groups. --- Mathematics --- Mathematical Analysis. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Spaces, Topological --- Compact groups --- Topological groups