Characteristic 0 Resolution of the Weyl Module in the Event of Partitioning (4, 4, 3)

Abstract

Let R be a commutative ring with 1, Ӻ be a free R-module and Ḍ_į be "the divided power algebra" of degree į. Ṃ is a left-graded module with for Ѡ = Ƶ_21^ҝ⋵ Å and Ѵ ⋵〖 Ḍ〗_(ᴯ_1 )⊗ Ḍ_(ᴯ_2 ) .Consequently, we have Ѡ(Ѵ)= Ƶ_(21 )^ҝ (Ѵ)=〖 ∂〗_(21 )^ҝ (Ѵ). where the separator ẋ vanishes between Ƶ_ḁᵬ^((ț))and ∂_ḁᵬ^((ț)). We depend on the definition of the mapping Cone and applying that for the partition (4, 4, 3) to find the resolution of the Weyl module for characteristic 0 "in the situation of partition (4, 4, 3) without depends on the resolution of the Weyl module for characteristic free". Also by using Capelli identities we prove the sequences and the subsequences of the terms of characteristic zero satisfy the mapping Cone. Finally by the commutative of each diagram in these sequences and subsequences we get the reduction of the terms of the resolution of the Weyl module for characteristic free to the terms of the resolution of the Weyl module for characteristic 0.

Keywords

• mapping cone,,
• ,،divided power algebra,,
• ,،place polarization,,
• ,،resolution of weyl module