In this paper, using Bourbaki's convention, we consider a simple Lie algebra $\mathfrak{g}\subset \mathfrak{g}{\mathfrak{l}}_m$ of type B, C or D and a parabolic subalgebra $\mathfrak{p}$ of $\mathfrak{g}$ associated with a Levi factor composed essentially, on each side of the second diagonal, by successive blocks of size two, except possibly for the first and the last ones. Extending the notion of a Weierstrass section introduced by Popov to the coadjoint action of the truncated parabolic subalgebra associated with $\mathfrak{p}$, we construct explicitly Weierstrass sections, which give the polynomiality (when it was not yet known) for the algebra generated by semi-invariant polynomial functions on the dual space ${\mathfrak{p}}^{⁎}$ of $\mathfrak{p}$ and which allow to linearize semi-invariant generators. Our Weierstrass sections require the construction of an adapted pair, which is the analogue of a principal $\mathfrak{s}{\mathfrak{l}}_2$-triple in the non reductive case.

在本文中，使用Bourbaki的约定，我们考虑一个简单的李代数 $\mathfrak{G}\subset \mathfrak{G}{\mathfrak{升}}_{米}$ B，C或D类型和抛物子代数 $\mathfrak{p}$ 的 $\mathfrak{G}$与Levi因子相关的元素基本上在第二对角线的每一侧上由大小为2的连续块组成，除了第一个和最后一个块外。将Popov引入的Weierstrass部分的概念扩展到与$\mathfrak{p}$，我们显式构造了Weierstrass部分，给出了由对偶空间上的半不变多项式函数生成的代数的多项式（当未知时） ${\mathfrak{p}}^{⁎}$ 的 $\mathfrak{p}$并允许线性化半不变发电机。我们的Weierstrass部分需要构造一个适应对，这与原理类似$\mathfrak{s}{\mathfrak{升}}_{\mathrm{2个}}$-在非归约情况下为三倍。