# Geometrical Equivalence and Action Type Geometrical Equivalence of Group Representations

## TL;DR

This paper demonstrates that action-type geometrical equivalence and group geometrical equivalence do not necessarily imply overall geometrical equivalence of group representations, highlighting limitations in current equivalence criteria.

## Contribution

It provides a counterexample showing the non-implication between different types of geometrical equivalences in group representations.

## Key findings

- Counterexample disproves the implication from action-type to overall geometrical equivalence.
- Highlights the independence of different geometrical equivalence notions in group representations.
- Clarifies limitations in the criteria for classifying group representations based on geometrical equivalence.

## Abstract

In this paper we present the example which proves that we can not conclude the geometrical equivalence of group representations from the corresponding action-type geometrical equivalence and group geometrical equivalence.