RGD-systems over $\mathbb{F}_2$

TL;DR

This paper characterizes the existence of RGD-systems over the finite field  with specific commutation relations, providing a method to construct new examples and exploring their applications.

Contribution

It establishes necessary and sufficient conditions for RGD-systems over , linking Weyl-invariance of relations to realizability in the group U+ and enabling new constructions.

Findings

Existence of RGD-systems over  is equivalent to Weyl-invariance of relations.

Provides a framework to generate new RGD-systems with complex relations.

Discusses applications of the constructed RGD-systems.

Abstract

In this paper we prove that an RGD-system over $\mathbb{F}_2$ with prescribed commutation relations exists if and only if the commutation relations are Weyl-invariant and can be realized in the group $U_+$. This result gives us a machinery to produce new examples of RGD-systems with complicated commutation relations. We also discuss some applications of this result.