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Representations of a Group I

Chapter
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 78)

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).

Keywords

Irreducible Representation Invariant Subspace Unitary Representation Product Representation Irreducible Character 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  1. 1.Japan Women’s UniversityBunkyo-ku, Tokyo 112Japan
  2. 2.Department of Physics, School of Science and TechnologyMeiji UniversityTama-ku, Kawasaki 214Japan

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