Abstract
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).
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© 1990 Springer-Verlag Berlin Heidelberg
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Inui, T., Tanabe, Y., Onodera, Y. (1990). Representations of a Group I. In: Group Theory and Its Applications in Physics. Springer Series in Solid-State Sciences, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80021-4_4
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DOI: https://doi.org/10.1007/978-3-642-80021-4_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60445-7
Online ISBN: 978-3-642-80021-4
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