This paper describes a construction of a minimal free resolution of a generic ideal defined by determinants in characteristic zero. It produces not only the free modules in the resolution, but it also defines the maps between them explicitly and in detail in terms of idempotents in the group algebra of the symmetric group.
"A minimal free complex associated to the minors of a matrix." J. Commut. Algebra 10 (2) 213 - 242, 2018. https://doi.org/10.1216/JCA-2018-10-2-213