Lifting mappings over invariants of finite groups

TL;DR

This paper characterizes when maps into the orbit space of a finite group representation can be lifted to the original space, with special focus on complex reflection groups, providing criteria for such lifts.

Contribution

It provides a detailed characterization of liftability of maps into orbit spaces of finite groups, especially for complex reflection groups, extending understanding of invariants and mappings.

Findings

Criteria for liftability of maps into orbit spaces

Special results for complex reflection groups

Conditions for regular, holomorphic, or formal lifts

Abstract

We characterize those regular, holomorphic or formal maps into the orbit space $V/G$ of a complex representation of a finite group $G$ which admit a regular, holomorphic or formal lift to the representation space $V$. In particular, the case of complex reflection groups is investigated.