Look at the short paper MR902299 (89a:17012) 17B10 (20C30) Zelevinski˘ı, A.V. [Zelevinsky, Andrei] (2-AOS-CY), Resolutions, dual pairs and character formulas. (Russian) Funktsional. Anal. i Prilozhen. 21 (1987), no. 2, 74–75, as well as the independent work by Kaan Akin (a former student of David Buchsbaum) including MR1194310 (94e:20059) 20G05 Akin, Kaan (1-OK), On complexes relating the Jacobi-Trudi identity with the Bernstein-Gel0fand-Gel0fand resolution. II. J. Algebra 152 (1992), no. 2, 417–426. I'm not aware of any later refinements A further refinement is given in MR1379204 (97b:20066) 20G05 Maliakas, Mihalis (1-AR), Resolutions and parabolic Schur algebras. J. Algebra 180 (1996), no. 3, 679–690.