Score for the Partition (9,8,3)

Abstract

The Weyl module resolution studied by Buchsbaum where the Weyl module  is the image of the Weyl map  for the skew-partition  and  is a free module defined on a commutative ring  with identity; 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  

The reduction from the terms of the characteristic-free of Weyl module resolution to the terms of the Lascoux resolution found in this work for the partition (9,8,3) by using the boundary maps and prove that the sequence of the reduction terms is exact.