A construction of pseudo-reductive groups with non-reduced root system

TL;DR

This paper constructs specific pseudo-reductive groups with non-reduced root systems of type BC_n in characteristic 2 and provides formulas for their irreducible module dimensions.

Contribution

It introduces a simple construction method for pseudo-split pseudo-simple groups of type BC_n in characteristic 2, expanding understanding of their structure.

Findings

Constructed pseudo-reductive groups with non-reduced root systems

Derived formulas for dimensions of irreducible modules

Identified existence conditions in characteristic 2

Abstract

We describe a straightforward construction of the pseudo-split absolutely pseudo-simple groups of minimal type with irreducible root systems of type $BC_n$; these exist only in characteristic $2$. We also give a formula for the dimensions of their irreducible modules.