Presentation for parabolic subgroups of GL_n(F_2)

TL;DR

This paper introduces a new two-dimensional Coxeter system framework to describe parabolic subgroups of GL_n(F_2), providing a novel algebraic perspective on their structure.

Contribution

It presents the concept of two-dimensional Coxeter systems and applies it to characterize parabolic subgroups of GL_n(F_2).

Findings

Parabolic subgroups of GL_n(F_2) can be described using two-dimensional Coxeter systems.

The notion of two-dimensional Coxeter systems is introduced and shown to be effective.

Provides a new algebraic tool for studying subgroup structures in linear groups.

Abstract

We introduce the notion of two-dimensional Coxeter system and show that parabolic subgroups of GL_n(F_2) can be described by an appropriate two-dimensional Coxeter system.