Abstract:
We introduce a class of equivariant vector bundles on isotropic symplectic Grassmannians $\operatorname{IGr}(k,2n)$ 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 $\operatorname{IGr}(k,2n)$. 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 $\operatorname{IGr}(3,2n)$.
Bibliography: 11 titles.
Keywords:isotropic Grassmannians, staircase complexes, equivariant resolutions, exceptional collections in the derived categories of coherent sheaves.
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