Symmetries of special 2-flags

TL;DR

This paper derives recursive relations for all infinitesimal symmetries of special 2-flags, advancing the understanding of their classification and revealing a continuous modulus in length seven.

Contribution

It provides the first recursive formulas for infinitesimal symmetries of special 2-flags, filling a gap in the classification theory since 2010.

Findings

Recursive relations for symmetries derived

Classification completed for lengths up to four

Existence of a continuous modulus in length seven

Abstract

This work is a continuation of authors' research interrupted in the year 2010. Derived are recursive relations describing for the first time all infinitesimal symmetries of special 2-flags (sometimes also misleadingly called `Goursat 2-flags'). When algorithmized to the software level, they will give an answer filling in the gap in knowledge as of 2010: on one side the local finite classification of special 2-flags known in lengths not exceeding four, on the other side the existence of a continuous numerical modulus of that classification in length seven.