Actions of a group of prime order without equivariantly simple germs

TL;DR

This paper proves that equivariantly simple invariant singularities are rare and only occur for specific representations of prime order groups, especially in real or nearly real cases.

Contribution

It establishes the limited conditions under which equivariantly simple invariant singularities can exist for prime order groups.

Findings

Equivariantly simple invariant singularities are restricted to certain real and near-real representations.

Such singularities only occur in very specific cases for groups of prime order.

The results narrow down the possible representations admitting these singularities.

Abstract

We prove that equivariantly simple invariant singularities can only exist for very few representations of a group of prime order: for real representations and some ``almost, but not quite real'' representations.