# finite dimensional modules are highest weight modules [closed]

Let $$\mathfrak{g}$$ be a basic classical simple Lie super algebra. I want to prove that every finite dimensional module over $$\mathfrak{g}$$ has a highest weight vector.

My feeling is, since $$e_i$$'s are rising operators it will kill a non-zero vector and this will give us a highest weight vector and may be we need to use Lie's theorem.

But I am unable to connect these things to get a perfect answer. If some one can tell me clearly what is happening here, that would help me a lot. Thank you.

• There are books out there that handle this stuff. This is hardly a research level question.
– user130903
Nov 6, 2018 at 8:02