Ulrich Schur bundles on flag varieties

TL;DR

This paper investigates the existence and classification of Ulrich bundles arising from Schur functors on partial flag varieties, providing new classifications and conjectures for specific cases.

Contribution

It classifies Ulrich bundles of this form on certain two-step flag varieties and shows non-existence on varieties with three or more steps.

Findings

No Ulrich bundles of this form exist on flag varieties with three or more steps.

Complete classification of such bundles on specific two-step flag varieties.

Conjectural description of which two-step flag varieties admit these Ulrich bundles.

Abstract

In this paper, we study equivariant vector bundles on partial flag varieties arising from Schur functors. We show that a partial flag variety with three or more steps does not admit an Ulrich bundle of this form with respect to the minimal ample class. We classify Ulrich bundles of this form on two-step flag varieties F(1,n-1;n), F(2,n-1;n), F(2,n-2;n), F(k,k+1;n) and F(k,k+2;n). We give a conjectural description of the two-step flag varieties which admit such Ulrich bundles.