Induced characters refer to representations of a group that arise from the representation of a subgroup. In the context of representation theory—an area of mathematics that studies abstract algebraic structures through linear transformations—induced characters are a way to construct new representations of a group via a subgroup.
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For a character of , the induced character isThis is the character of a representation of . Substituting this expression into the character inner product and putting proves Frobenius reciprocity.