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- Title
On Free Resolution of Weyl Module and Zero Characteristic Resolution in the Case of Partition (7,5,3).
- Authors
Raheem, Ghsoon Rabeea; Hassan, Haytham Razooki
- Abstract
The characteristic-free resolution of K(7,5,3) is applied to the Lascoux resolution of K(7,5,3)F (characteristic zero resolution) in this paper. This research teaches us about the relationship between the resolution of the weyl module K(7,5,3)F in the characteristic-free mode and the Lascoux mode. In this work, let R be a commutative ring with 1, Ӻ be a free R-module and Ḍį be "the divided power algebra" of degree į. Ṃ is a left-graded module with for Ѡ = Ƶ21ҝ ⋵ Å and Ѵ ⋵ Ḍᴯ1 ⊗ Ḍᴯ2. We have Ѡ(Ѵ)= Ƶ21ҝ (Ѵ) = ∂21ҝ (Ѵ). where the separator ẋ vanishes between Ƶḁᵬ(ț)and ∂ḁᵬ(ț). Also by using Capelli identities we prove the sequences and the subsequences of the terms of characteristic zero satisfy the commutative for each diagram in these sequences and subsequences. Finally 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.
- Subjects
MODULES (Algebra); FREE resolutions (Algebra); HOMOLOGICAL algebra; COMMUTATIVE rings; RING theory
- Publication
Journal of University of Anbar for Pure Science, 2023, Vol 17, Issue 2, p317
- ISSN
1991-8941
- Publication type
Article
- DOI
10.37652/juaps.2023.141655.1096