The Frobenius Reciprocity Theorem is a result of representation theory expressing a duality between the operations of restricting a representation of a group to a subgroup and inducing a representation of the group from one of the subgroup. Named for Ferdinand Georg Frobenius, who founded the representation theory of finite groups, it is a central tool for using knowledge about a subgroup's representations to find and classify the representations of a larger group containing it.
Facts
StatementFrobenius reciprocity is a duality between restricting a representation of a group to a subgroup and inducing a representation of the group from a representation of the subgroup. 1 Classification
Statement Form Sources
1. Frobenius reciprocity, Wikipedia
IntroductionQuote, Introduction
Frobenius reciprocity is a theorem expressing a duality between the process of restricting and inducing.
2. Ferdinand Georg Frobenius, MacTutor History of Mathematics
BiographyQuote, Biography
In 1898 he introduced the notion of induced representations and the Frobenius Reciprocity Theorem
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