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.



finite dimensional modules are highest weight modules
This is contained in section 1.5.3 of the book "Dualities and representations of Lie superalgebras" by Cheng and Wang. Chapter 1 of their book happens to be available for free on the AMS bookstore website: <https://bookstore.ams.org/gsm-144>.


