We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite groups. We prove the Bernstein inequality for these rings. Our main tool is the filter dimension introduced by Bavula. We extend the results for the invariants of the Weyl algebra with respect to the symplectic action of a finite group, for the rings of invariant differential operators on quotient varieties, and invariants of certain generalized Weyl algebras under the linear actions. We show that the filter dimension of all above mentioned algebras equals 1.

中文翻译：

---

不变微分算子环的完整模块

我们研究了具有有限克鲁尔维数的仿射交换域上不变微分算子环关于有限群的任意动作的完整模块。我们证明了这些环的伯恩斯坦不等式。我们的主要工具是 Bavula 引入的过滤器维度。我们扩展了外尔代数关于有限群的辛作用的不变量的结果，对于商群上的不变微分算子的环，以及某些广义外尔代数在线性作用下的不变量的结果。我们证明了上述所有代数的过滤器维度都等于 1。