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 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Frobenius reciprocity, Wikipedia
Proved By
Source Frobenius reciprocity, Wikipedia
Sources
1. Frobenius reciprocity, Wikipedia
Introduction
Frobenius reciprocity is a theorem expressing a duality between the process of restricting and inducing.
In Branch: Representation Theory, Lead sentence
In mathematics, and in particular representation theory, Frobenius reciprocity is a theorem expressing a duality between the proce
Proved By: Ferdinand Georg Frobenius, Lead paragraph
In mathematics, and in particular representation theory, Frobenius reciprocity is a theorem expressing a duality between the process of restricting and inducing. It can be used to leverage
View the Source2. 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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