20191024 04:57:07 0600  asked a question  Vector subspaces of Verma Modules I know how to construct ordinary vector spaces over fields. For example a vector space of dimension 4 over rationals: Given a set of linearly independent elements, we can construct the subspace of V formed by that set. For example we can construct the subspace whose basis is {$(1,0,0,0), (0,1,0,0)$}: Now we given $u\in U$, we can also find its coordinates with respect to the basis {$(1,0,0,0), (0,1,0,0)$}. For example, if we take the vector $(2,2,0,0)\in U$: I want to do something similar with Verma Modules. So given a linearly independent set and a vector, I want to get its coordinates w.r.t this basis. So first let's construct a Verma Module over $\frak{sp}(4)$: Let $v$ be the highest weight vector. I want to construct the $\mathbb{Q}$subspace of $M$ spanned by a given basis. For example I tried to construct a subspace with basis {$y_1^2\cdot v, y_2^3\cdot v$}. So quite naively I tired: which gave a big error message. Is there a way to solve this problem? On a related note, is there any way to check if a given set of elements in a Verma module are linearly independent? 
20191014 20:43:47 0600  answered a question  sage8.9 fails compilation in Ubuntu 18.04 I recently installed SAGE on ubuntu 18.04. This command worked for me Check http://www.sagemath.org/downloadlinu... (go to the distributions section) 
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20191014 19:33:14 0600  asked a question  Verma modules and accessing constants of proportionality The Math Part: Let me first describe the math without going into the programming. Start with two vectors $v$ and $w$ in a vector space (just a regular vector space with no additional structure). Let's say we know that $w=\lambda\cdot v$ for some scalar $\lambda$. Given $w$ and $v$, can we figure out what $\lambda$ is? The Programming Part: Now let me describe specifics of my calculation. I am working with a Verma Module over $\frak{sp}(4)$. We will call the highest weight vector $v$. In code, Now we have $x_2y_2\cdot v=3\cdot v$ and $x_2^2y_2^2\cdot v= 24\cdot v$. So in code, In general, we will have $$x_2^ny_2^n\cdot v=c_n\cdot v$$ for some constant $c_n$ (with $c_1=3$ and $c_2=24$). My questions is the following. How to access this constant $c_n$, given that we know $v$ and $c_n\cdot v$? 
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20190930 18:17:44 0600  commented answer  Questions about Lie algebra Thanks for the answer. I have one further question, when you are writing 
20190930 03:44:33 0600  asked a question  Questions about Lie algebra I am trying to do some calculations and I don't understand what the output is. The output is the following

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20190924 02:49:33 0600  asked a question  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 $L(\lambda)=W_\lambda/N_\lambda$.
Could you please help me with the syntax? Thanks is advance. 