Representations of a Group I
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In this and the following chapter, we shall develop the theory of representations of finite groups. We begin with the definition of group representations and related fundamental concepts (Sect. 4.1), and follow this with examples of representations (Sects. 4.2, 4.4). Between the examples (Sect. 4.3), effects of symmetry transformation operators on functions are considered. After having become familiar with group representations from these examples, we present the general representation theory (Sects 4.5–13). Several theorems, such as Schur’s lemma and orthogonality theorems, appear at this stage. Most of their proofs are given at the end of the chapter (Sect. 4.13).
KeywordsIrreducible Representation Invariant Subspace Unitary Representation Product Representation Irreducible Character
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