Secondary staircase complexes on isotropic Grassmannians

Abstract

We introduce a class of equivariant vector bundles on the isotropic symplectic Grassmannians $\mathrm{IGr}(k,2n)$ defined as appropriate truncations of staircase complexes, and we show that these bundles can be assembled into a number of complexes quasi-isomorphic to symplectic wedge powers of the symplectic bundle on $\mathrm{IGr}(k,2n)$. We are planning to use these secondary staircase complexes to study the fullness of exceptional collections in the derived categories of isotropic Grassmannians and Lefschetz exceptional collections on $\mathrm{IGr}(3,2n)$.