# Computations on Verma Modules

I want to do some computation on Verma Modules. Consider the Verma Module $W_\lambda$ of weight $\lambda$. We know that $W_\lambda$ has a unique maximal submodule $N_\lambda$ and a corresponding irreducible quotient $L(\lambda)=W_\lambda/N_\lambda$.

- I found some documentation about Verma Modules on the SAGE website. But it does not tell how to find the irreducible quotient. I want to figure out this quotient $L(\lambda)$.
- Secondly, I want to see know the dimensions of weight spaces of $W_\lambda$ and $L(\lambda)$ and what they look like explicitly.

Could you please help me with the syntax? Thanks is advance.

Struggling with this right now too, not currently sure but think that using theorem 2 in this http://www.math.columbia.edu/~woit/LieGroups-2012/vermamodules.pdf (http://www.math.columbia.edu/~woit/Li...) and working out the exact sequence might be an approach. Unfortunately quotient modules seem not to be implemented yet so not sure if that's a dead end.