Testing chirality on hypertopes

TL;DR

This paper establishes group-theoretical criteria for identifying chiral hypertopes in coset geometries, enabling analysis of larger structures and advancing theoretical understanding without constructing incidence graphs.

Contribution

It introduces new group-theoretical conditions for recognizing chiral hypertopes, simplifying the analysis process and expanding the scope of study for larger coset geometries.

Findings

Provides criteria to identify chiral hypertopes without incidence graph construction

Enables computational study of larger coset geometries

Facilitates theoretical proofs about chiral hypertopes

Abstract

In this paper we give group-theoretical conditions on the maximal parabolic subgroups of a coset geometry for it to be a chiral hypertope, bypassing the need to construct the incidence graph of the coset geometry to determine whether or not it is a chiral hypertope. This result permits to study much larger coset geometries with computers and gives hope on proving theoretical results about coset geometries that are chiral hypertopes.