Lemma (Schur’s lemma).
Note that both the kernel, , and the image, , are -submodules of and , respectively. Since is irreducible, is either trivial or all of . In the former case, is all of — also because is irreducible — and hence is invertible. In the latter case, is the zero map. ∎
One of the most important consequences of Schur’s lemma is the following.
|Date of creation||2013-03-22 13:08:01|
|Last modified on||2013-03-22 13:08:01|
|Last modified by||rmilson (146)|