AI 中文总结
该论文证明非本原复反射群G(r,p,n)上不变微分算子的一致分解定理，给出单分量的显式生成元，推广实反射群相关结果，还通过伽罗瓦下降给出单分量的第二种描述。
AI 中文摘要
我们研究多项式环在判别式处局部化后的模结构，该多项式环定义在非本原复反射群G(r,p,n)的不变量环上，我们利用Ariki–Terasoma–Yamada高阶Specht多项式给出了其单分量的显式生成元。证明依赖于计算G(r,p,n)判别式的雅可比引理，结合双中心化子论证。作为特例，当r=2、p=2或p=1时，我们得到了实反射群W(Dₙ)和W(Bₙ)的已知分解定理，并大幅缩短了其证明；我们还明确处理了G(r,r,n)和G(r,1,n)，给出了具体例子（D₂、D₃、B₂）及其中心幂等元。最后，首次将Nonkané的范畴伽罗瓦下降等价应用于G(r,p,n)，以扭曲不变量的形式给出了单分量的第二种无生成元描述。
英文摘要
{We study the module structure of the polynomial ring, localized at the discriminant, over the ring of differential operators on the ring of invariants of the imprimitive complex reflection group $G(r,p,n)$, describing its simple components with explicit generators given by the higher Specht polynomials of Ariki--Terasoma--Yamada. The proof rests on a Jacobian lemma computing the discriminant of $G(r,p,n)$, combined with a double-centralizer argument. As particular cases ($r=2$, $p=2$ or $p=1$) we recover, and considerably shorten, the known decomposition theorems for the real reflection groups $W(D_n)$ and $W(B_n)$; we also treat $G(r,r,n)$ and $G(r,1,n)$ explicitly, with worked examples ($D_2$, $D_3$, $B_2$) and their central idempotents. Finally, applying the Galois descent equivalence of categories of Nonkané to $G(r,p,n)$ for the first time gives a second, generator-free description of the simple summands as twisted invariants.}
