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Representations and Characters of Groups, Second Edition by Martin Liebeck, Gordon James

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9

Schur’s Lemma

Schur’s Lemma is a basic result concerning irreducible modules. Though simple in both statement and proof, Schur’s Lemma is fundamental to representation theory, and we give an immediate application by determining all the irreducible representations of finite abelian groups.

Schur’s Lemma concerns imageG-modules rather than imageG-modules, and since much of the ensuing theory depends on it, we shall deal with imageG-modules for the remainder of the ...

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