In the representation theory of finite groups, a vector space equipped with a group that acts by linear transformations of the space is called a linear representation of the group. A linear map that commutes with the action is called an intertwiner. That is, an intertwiner is just an equivariant linear map between two representations. Alternatively, an intertwiner for representations of a group G over a field K is the same thing as a module homomorphism of K [ G ] - modules, where K [ G ] is the group ring of G.