The two rows resolution of Weyl module in the cases partition (12,6)

Let ℱ be a free R-module, where R is a commutative ring with 1 and D_nF be the nth degree divided power, the place polarization technique is a combinatorial approach for computing the complex elements. 〖∂_ 〗_21^((k)) is a location polarization that occurs from place one to place two.The induction argument on the amount of overlaps between the two rows give us a description of the result that we want, and give us an answer of what kind of resolution of Koszul-like complex (we called arithmetic Koszul Complex).Weyl module K_(λ/μ) ℱ = 𝐼𝑚 ( 〖d ' 〗_(λ⁄μ )), where 〖d ' 〗_(λ⁄μ)and 〖d ' 〗_(λ⁄μ) :〖Ɒ 〗_(λ⁄μ)ℱ ⟶ _(〖 ^Λ〗_(λ̃ ⁄ μ̃) ) F is the Weyl map, from which the term "Weyl module" will be derived.In this paper, we will focus on studying the two rows Weyl module resolution for the partition (12,6) by using homological diagram, contracting homotopy and place polarization.