ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 21 Sep 2020 16:48:03 -0500Computations on Verma Moduleshttps://ask.sagemath.org/question/48042/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 $L(\lambda)=W_\lambda/N_\lambda$.
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.Mon, 23 Sep 2019 18:44:47 -0500https://ask.sagemath.org/question/48042/computations-on-verma-modules/Comment by IntegrableSystems for <p>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 $L(\lambda)=W_\lambda/N_\lambda$. </p>
<ol>
<li>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 $L(\lambda)$. </li>
<li>Secondly, I want to see know the dimensions of weight spaces of $W_\lambda$ and $L(\lambda)$ and what they look like explicitly.</li>
</ol>
<p>Could you please help me with the syntax? Thanks is advance.</p>
https://ask.sagemath.org/question/48042/computations-on-verma-modules/?comment=53532#post-id-53532Struggling 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 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.Mon, 21 Sep 2020 16:48:03 -0500https://ask.sagemath.org/question/48042/computations-on-verma-modules/?comment=53532#post-id-53532