Remark 2

Let M be an isotypical A-module of type S, and let $(V, \alpha )$ be a description of M. Let B be a subring of the ring End$_A(M)^o$. The ring isomorphism from End$_D(V)^o$ to End$_A(M)^o$ endows V with the structure of a $(D$, B)-bimodule, so that $\alpha$ is an isomorphism of $(A$, B)-bimodules. There exists an isomorphism from the set of $(D$, B)-sub-bimodules of V, ordered by inclusion, to the set of $(A$, B)-sub-bimodules of M (VIII, p. 62, Theorem 2 and VIII, p. 63, Corollary 2).