  This article deals with computing the cohomology of Schur functors applied to
tautological bundles on super Grassmannians. We show that in a range of cases,
the cohomology is a free module over the cohomology of the structure sheaf and
that the space of generators is an irreducible representation of the general
linear supergroup that can be constructed via explicit multilinear operations.
Our techniques come from commutative algebra: we relate this cohomology
calculation to Tor groups of certain algebraic varieties.
