##  [Frobenius Reciprocity](/frobenius-reciprocity) 

  ##  [Frobenius Reciprocity](https://puremath.quantumdictionary.io/frobenius-reciprocity-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An adjunction statement in representation theory asserting a canonical isomorphism between Hom-spaces: for a subgroup H of G and suitable representations V of H and W of G, Hom_G(Ind_H^G V, W) ≅ Hom_H(V, Res_H^G W); equivalently, induction is left adjoint to restriction.

 

 

 

 

 





 

 



 ##  [Frobenius Reciprocity](https://algebra.quantumdictionary.io/frobenius-reciprocity-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A natural adjunction between induction and restriction functors in representation theory: for a subgroup H of a group G (or more generally for a pair of algebras and a module restriction/extension situation) there is a canonical isomorphism Hom_G(Ind_H^G V, W) ≅ Hom_H(V, Res^G_H W) identifying G-maps from an induced representation with H-maps into the restricted representation.