Computations on Verma Modules

asked 2019-09-23 20:36:09 -0500

slartibartfast gravatar image

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 $L(\lambda)=W_\lambda/N_\lambda$.

  1. 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 $L(\lambda)$.
  2. 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.

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Comments

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.

IntegrableSystems gravatar imageIntegrableSystems ( 2020-09-21 16:48:03 -0500 )edit