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arXiv · 2511.12569

The Regular property of Invariant Rings over Regular Domains

Shubham Jaiswal·Tony J. Puthenpurakal
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Abstract

The main result of this paper is a generalization of the theorem of Chevalley-Shephard-Todd to the rings of invariants of pseudo-reflection groups over regular domains. More precisely, let $A$ be a regular domain and let $K$ be its field of fractions. Let $G\subseteq GL_n(A)$ be a finite group. Let $G$ act linearly on $A[X_1,X_2,\dots, X_n]$ (fixing $A$). Assume that $|G|$ is invertible in $A$. We prove that $G\subseteq GL_n(K)$ is generated by pseudo-reflections if and only if $(A[X_1,X_2,\dots, X_n])^G$ is regular.

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Shubham Jaiswal, Tony J. Puthenpurakal. 2025-11-16. The Regular property of Invariant Rings over Regular Domains. https://arxiv.org/abs/2511.12569

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