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Group theory --- Q-groups. --- Representations of groups.

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The Representation Theory of the Symmetric Group provides an account of both the ordinary and modular representation theory of the symmetric groups. The range of applications of this theory is vast, varying from theoretical physics, through combinatories to the study of polynomial identity algebras; and new uses are still being found.

Symmetry groups. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Groups, Symmetry --- Symmetric groups --- Crystallography, Mathematical --- Quantum theory --- Representations of groups

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The most important examples of finite groups are the group of permutations of a set of n objects, known as the symmetric group, and the group of non-singular n-by-n matrices over a finite field, which is called the general linear group. This book examines the representation theory of the general linear groups, and reveals that there is a close analogy with that of the symmetric groups. It consists of an essay which was joint winner of the Cambridge University Adams Prize 1981-2, and is intended to be accessible to mathematicians with no previous specialist knowledge of the topics involved. Many people have studied the representations of general linear groups over fields of the natural characteristic, but this volume explores new territory by considering the case where the characteristic of the ground field is not the natural one. Not only are the results in the book elegant and interesting in their own right, but they suggest many lines for further investigation.

Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Representations of groups --- 512.547 --- 512.547 Linear representations of abstract groups. Group characters --- Linear representations of abstract groups. Group characters

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Representations of algebras --- Representations of Lie algebras --- Representations of Lie groups --- Ordered algebraic structures --- Lie algebras --- Lie groups --- Representations of groups --- Tables

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Partial differential operators --- Commutation relations (Quantum mechanics) --- Representations of Lie groups --- Lie groups --- Representations of groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Differential operators --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Commutative algebra --- Quantum theory --- Partial differential operators. --- Representations of Lie groups. --- Commutation relations (Quantum mechanics). --- Lie, Algèbres de --- Lie, Groupes de --- Opérateurs linéaires --- Opérateurs, Théorie des