The thought process that led me to this question is that the identity 
$$ \left(\prod\_i \frac1{1-x\_i}\right)\left(\prod\_i {1-x\_i}\right)=1$$
can be understood as expressing exactness of the Koszul complex.
This identity is rewritten by taking $\left(\prod\_i \frac1{1-x\_i}\right)$
as the generating function for the complete symmetric functions $h\_n$
and $\left(\prod\_i {1+x\_i}\right)$ as the generating function for the elementary symmetric functions $e\_n$.


Next we have the Jacobi-Trudi identity which expresses a Schur function as the determinant of a matrix whose entries are complete (or elementary) symmetric functions. Also the Specht module is sometimes constructed as a quotient (or submodule) of the trivial representation of the Young subgroup induced to a representation. This suggests that this is the start of a BGG resolution.


I imagine that if this works then it is well-known. Could I have some references? and where does line of thought lead?



Can the Jacobi-Trudi identity be understood as a BGG resolution?
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. 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.


