Computations on Verma Modules

asked 5 years ago

slartibartfast gravatar image

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

  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(λ).
  2. Secondly, I want to see know the dimensions of weight spaces of Wλ and L(λ) and what they look like explicitly.

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

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Comments

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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 ( 4 years ago )