is endowed with the Jacobson topology. (See [@Dixmier2], [@Dixmier3], [@BorhoGabrielRentschler] for the details.)

In addition, it is well known that the following conditions on an ideal $J\subset U({\mathfrak{n}})$ are equivalent[@Dixmier3 Proposition 4.7.4, Theorem 4.7.9]: $$\begin{split}
&\text{i) $J$ is \label{formula:conditions_Prim_fd}primitive;}\\
&\text{ii) $J$ is maximal;}\\
&\text{iii) the center of $U({\mathfrak{n}})/J$ is trivial;}\\
&\text{iv) $U({\mathfrak{n}})/J$ is isomorphic to a Weyl algebra of finitely many variables.}
\end{split}$$ Recall that the Weyl algebra ${\mathcal{A}}_s$ of $2s$ variables is the unital associative algebra with generators $p_i$, $q_i$ for $1\leq i\leq s$, and relations $[p_i,q_i]=1$, $[p_i,q_j]=0$ for $i\neq j$, $[p_i,p_j]=[q_i,q_j]=0$ for all $i,~j$. Furthermore, in conditions (\[formula:conditions\_Prim\_fd\]) we have $U({\mathfrak{n}})/J\cong{\mathcal{A}}_s$ where $s$ equals one half of the dimension of the coadjoint $N$-orbit of $\lambda$, given that $J=J(\lambda)$.

Before formulating our first main result, we will present the classification of centrally generated primitive ideals of $U({\mathfrak{n}})$ for $A_{n-1}$ and $C_n$ from [@IgnatyevPenkov1]. Recall the definition of the Kostant cascade ${\mathcal{B}}$ from Subsection \[sst:center\_fd\]. Let $\Delta\subset\Phi^+$ be the set of simple roots, i.e., $$\Delta=\begin{cases}\{{\epsilon}_1-{\epsilon}_2,~\ldots,~{\epsilon}_{n-1}-{\epsilon}_n\}&\text{for }\Phi=A_{n-1},\\
\{{\epsilon}_1-{\epsilon}_2,~\ldots,~{\epsilon}_{n-1}-{\epsilon}_n,~{\epsilon}_n\}&\text{for }\Phi=B_n,\\
\{{\epsilon}_1-{\epsilon}_2,~\ldots,~{\epsilon}_{n-1}-{\epsilon}_n,~2{\epsilon}_n\}&\text{for }\Phi=C_n,\\
\{{\epsilon}_1-{\epsilon}_2,~\ldots,~{\epsilon}_{n-1}-{\epsilon}_n,~{\epsilon}_{n-1}+{\epsilon}_n\}&\text{for }\Phi=C_n.
\end{cases}$$ Note also that $${\mathcal{B}}\setminus\Delta=\begin{cases}
\bigcup_{1\leq i\leq(n-1)/2}\{{\epsilon}_{i}-{\epsilon}_{n-i+1}\}&\text{for }\Phi=A_{n-1},\\
\bigcup_{1\leq i\leq n/2}\{{\epsilon}_{2i-1}+{\epsilon}_{2i+1}\}&\text{for }\Phi=B_n,\\
\bigcup_{1\leq i<n/2}\{{\epsilon}_{2i-1}+{\epsilon}_{2i+1}\}&\text{for }\Phi=D_n,\\
{\mathcal{B}}\setminus\{2{\epsilon}_n\}&\text{for }\Phi=C_n.
\end{cases}$$.

Let $\{e_{\alpha}^*,~\alpha\in\Phi^+\}$ be the basis of ${\mathfrak{n}}^*$ dual to the 