coadjoint orbit in ${\mathfrak{n}}^*$. Note that, according to the Kostant–Kirillov orbit method, the set of all unitary irreducible representations of the Lie group $\exp{\mathfrak{n}}$ is also in one-to-one correspondence with the set of all coadjoint orbits in ${\mathfrak{n}}^*$.

Suppose that ${\mathfrak{n}}$ is the nilradical of a Borel subalgebra ${\mathfrak{b}}$ of a complex finite-dimensional semisimple Lie algebra ${\mathfrak{g}}$. The description of the center $Z({\mathfrak{n}})$ of $U({\mathfrak{n}})$ goes back to J. Dixmier, A. Joseph and B. Kostant. It turns out that $Z({\mathfrak{n}})$ is a polynomial algebra whose generators are parametrized by the positive roots from the Kostant cascade ${\mathcal{B}}$, a certain strongly orthogonal subset of the set $\Phi^+$ of positive roots of ${\mathfrak{g}}$ with respect to ${\mathfrak{b}}$ (see Subsection \[sst:center\_fd\] for the precise definition). Let $\{e_{\alpha},~\alpha\in\Phi^+\}$ be a basis of ${\mathfrak{n}}$ consisting of root vectors. We say that a linear form $f\in{\mathfrak{n}}^*$ is a Kostant form if $f(e_{\alpha})=0$ for $\alpha\notin{\mathcal{B}}$ and $f(e_{\beta})\neq0$ for $\beta\in{\mathcal{B}}\setminus\Delta$, where $\Delta$ is the set of simple roots. Note that the coadjoint orbit of a Kostant form has maximal possible dimension. By definition, a primitive ideal $J$ of $U({\mathfrak{n}})$ is centrally generated if it is generated as an ideal by its intersection with $Z({\mathfrak{n}})$. It was proved in 