Derived-category proof of the Grassmannian splitting criterion

Establish a proof of Ottaviani’s Grassmannian splitting criterion (Theorem 1.14 for Gr(P^k, P^n)) using the derived-category approach in the style of Beilinson–Kapranov, analogous to the Ancona–Ottaviani method for projective spaces and quadrics.

Background

Beilinson’s and Kapranov’s descriptions of the derived categories of P^n and Q^n enable derived-category proofs of splitting criteria. Ancona–Ottaviani (1991) provided such proofs for projective spaces and quadrics.

Ottaviani (1989) established a cohomological splitting criterion for Grassmannians using representation-theoretic tools and Bott’s theorem. The authors ask whether an analogous derived-category proof can be developed for this Grassmannian criterion.