Automorphism group of flag varieties with non-reduced stabilizer

TL;DR

This paper investigates the automorphism groups of rational projective homogeneous varieties over algebraically closed fields of positive characteristic, extending classical results to cases with non-reduced stabilizers.

Contribution

It generalizes Demazure's classical result by determining the automorphism group scheme structure for varieties with possibly non-reduced parabolic stabilizers.

Findings

Determined the automorphism group scheme structure for these varieties.

Extended classical results to positive characteristic with non-reduced stabilizers.

Provided a comprehensive description of automorphism groups in this setting.

Abstract

We consider rational projective homogeneous varieties over an algebraically closed field of positive characteristic, namely quotients of a semi-simple group by a possibly non-reduced parabolic subgroup. We determine the group scheme structure of the neutral component of their automorphism group, generalizing the classical result of Demazure on automorphism groups of flag varieties.