Complete reducibility and Steinberg endomorphisms

TL;DR

This paper explores a generalization of G-complete reducibility within the framework of Steinberg endomorphisms for connected reductive algebraic groups over algebraically closed fields of positive characteristic, extending known rationality results.

Contribution

It introduces a new generalization of G-complete reducibility related to Steinberg endomorphisms and proves an extension of a rationality result in this context.

Findings

Extended a rationality result for Steinberg endomorphisms

Generalized G-complete reducibility concept

Provided theoretical framework for algebraic group endomorphisms

Abstract

Let G be a connected reductive algebraic group defined over an algebraically closed field of positive characteristic. We study a generalization of the notion of G-complete reducibility in the context of Steinberg endomorphisms of G. Our main theorem extends a special case of a rationality result in this setting.