A note on the automorphism group of Schubert varieties

TL;DR

This paper investigates the automorphism groups of Schubert varieties, showing that automorphisms of the Grassmannian fix a Schubert variety precisely when they fix specific elements of the defining flag.

Contribution

It extends previous results by characterizing automorphisms of Schubert varieties in terms of fixed elements of the defining flag.

Findings

Automorphisms of the Grassmannian fix a Schubert variety iff they fix certain flag elements.

Provides a criterion for automorphisms based on flag elements.

Extends known results on automorphism groups of Schubert varieties.

Abstract

In this work we extend some previously known results on the automorphism group of Schubert varieties. We consider the Schubert conditions which define a Schubert variety. An automorphism of the Grassmannian fixes a Schubert variety contained in it if and only if it fixes certain elements of the flag used to define the Schubert conditions.