The Weyl module resolution studied by Buchsbaum where the Weyl module ????λ⁄μ(ℱ) is the image of the Weyl map ???? ′ λ⁄μ(ℱ) for the skew-partition λ⁄μ and ℱ is a free module defined on a commutative ring ℛ with identity; where λ runs over all partitions λ = (λ1, λ2,… , λs). There are a number of classical formulas that express the formal character of the representation ℒλ(ℱ) in terms of standard symmetric polynomials. Such formulas are also valid for the more general representation modules {ℒλ⁄μ(ℱ)} associated to skew partition λ⁄μ; where μ ⊆ λ, where the set of all irreducible polynomial representations of general linear group GL????(ℱ) of degree ???? is described by the module {ℒλ(ℱ)} 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

Title

Babylonian Journal of Mathematics

Publisher

Babylonian Journal of Mathematics

Publisher Country

Iraq

Publication Type

Prtinted only

Volume

2024

Year

2024

Pages

152-170