Remark 1

The canonical description $\alpha_M$ of the A-module M is an isomorphism of left $(A$, B)-bimodules. By the corollary of Proposition 9, VIII, p. 71, the mapping $f\mapsto ($Hom(1$_{S_{\lambda}}, f$))$_{\lambda\in\mathscr{S}_M}$ from B to $\prod_{\lambda\in\mathscr{S}_M}$ End$_{D_{\lambda}}(V_{\lambda})$ is a ring isomorphism.