Overgroups of exterior powers of an elementary group. Levels

Abstract

We prove a first part of the standard description of groups $H$ lying between an exterior power of an elementary group ${\bigwedge }^m{E}_n(R)$ and a general linear group $G{L}_{\left(\genfrac{}{}{0ex}{}{n}{m}\right)}(R)$ for a commutative ring $R$, $2\in R^{\ast }$ and $n⩾3m$. The description uses the classical notion of a level: for every group $H$ we find a unique ideal $A$ of the ground ring $R$ which describes $H$.

This paper is a sequel of arXiv:1801.07918 for the first question "Levels"