Consequence for the Partition (9,9,3)

Abstract

Let  be a free module defined on the commutative ring  with identity. Buchsbaum studied the Weyl module resolution where the Weyl module  is the image of the Weyl map  for the skew-partition  ; where  runs over all partitions . There are a number of classical formulas that express the formal character of the representation  in terms of standard symmetric polynomials. Such formulas are also valid for the more general representation modules  associated to skew partition ; where , where the set of all irreducible polynomial representations of general linear group  of degree  is described by the module  

For the partition (9,9,3) by applying the boundary maps we reduction the terms of the characteristic-free of Weyl module resolution to the terms of the Lascoux resolution and prove that the sequence of the reduction terms is exact.