Outcome for the Partition (9,6,3)

Abstract

The set of all irreducible polynomial representations of general linear group  of degree  is described by the module ; 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 .

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

Reduction the terms of the resolution of the characteristic-free of Weyl module to the terms of the resolution of Lascoux by employing the boundary maps for the partition (9,6,3) and prove that the sequence of the reduction terms is exact.