  The Springer modules have a combinatorial property called ``coincidence of
dimensions,'' i.e., the Springer modules are naturally decomposed into
submodules with common dimensions. Morita and Nakajima proved the property by
giving modules with common dimensions whose induced modules are isomorphic to
the submodules of Springer modules. They proved that the induced modules are
isomorphic to the submodules, by showing the coincidence of their characters.
Our aim is to construct isomorphisms between the induced modules and their
corresponding submodules in a combinatorial manner. For this purpose, we show
lemmas, which are equivalent to the classical Schur's lemma in special cases.
We also give a procedure to construct isomorphisms, and explicitly construct
isomorphisms in the case of the Springer modules corresponding to Young
diagrams of two rows.
