The regular representation
Every group has a regular representation that can be constructed solely from knowledge of the group multiplication table. It has two miraculous properties. First, it allows us to determine the total number of irreducible representations that the group possesses. Second, it allows us to construct the character table of the group. We will prove and demonstrate the first property in this chapter, saving the second property for Chapter 48 (MakeCharacterTable).
KeywordsIrreducible Representation Regular Representation Multiplication Table Character Table Symmetry Theory
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