Ulrich partitions for two-step flag varieties

Abstract

Ulrich bundles play a central role in singularity theory, liaison theory and Boij–Söderberg theory. It was proved by the first author together with Costa, Huizenga, Miró-Roig and Woolf that Schur bundles on flag varieties of three or more steps are not Ulrich and conjectured a classification of Ulrich Schur bundles on two-step flag varieties. By the Borel–Weil–Bott theorem, the conjecture reduces to classifying integer sequences satisfying certain combinatorial properties. In this paper, we resolve the first instance of this conjecture and show that Schur bundles on $F\left(k,k+3;n\right)$ are not Ulrich if $n>6$ or $k>2$.