Secondary staircase complexes on isotropic Grassmannians

We introduce a class of equivariant vector bundles on isotropic symplectic Grassmannians IGr(k,2n) defined as appropriate truncations of staircase complexes and show that these bundles can be assembled into a number of complexes quasi-isomorphic to symplectic wedge powers of the symplectic bundle on 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 IGr(3,2n). Bibliography: 11 titles.