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

Abstract

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

arXiv comment22 pages; version accepted for publication in Transformation Groups; appendix added to show an alternative approach using a significant theorem in Conrad--Gabber--Prasad