Acyclicity of Schur complexes and torsion freeness of Schur modules.

Let R be a Noetherian commutative ring and M a R -module with pd R M ≤ 1 that has rank. Necessary and sufficient conditions were provided in [1] for an exterior power ∧ k M to be torsion free. When M is an ideal of R similar necessary and sufficient conditions were provided in [2] for a symmetric power S k M to be torsion free. We extend these results to a broad class of Schur modules L λ / μ M. En route, for any map of finite free R modules ϕ : F → G we also study the general structure of the Schur complexes L λ / μ ϕ , and provide necessary and sufficient conditions for the acyclicity of any given L λ / μ ϕ by computing explicitly the radicals of the ideals of maximal minors of all its differentials. [ABSTRACT FROM AUTHOR]