A simple parametrization for G2

TL;DR

This paper introduces a straightforward parametrization of the G2 group aligned with its SU(3) fibration structure and provides an explicit, simple expression for its invariant measure.

Contribution

It presents a new, simple parametrization of G2 and explicitly computes its invariant measure, facilitating easier calculations involving G2.

Findings

Derived a simple parametrization of G2 consistent with its SU(3) fibration

Explicitly computed the bi-invariant measure with a simple expression

Simplifies calculations involving G2 group structures

Abstract

We give a simple parametrization of the $G_2$ group, which is consistent with the structure of $G_2$ as a SU(3) fibration. We also explicitly compute the (bi)invariant measure, which turns out to have a simple expression.