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The two rows resolution of Weyl module in the cases partition (12,6) | ||
| Journal of University of Anbar for Pure Science | ||
| Volume 19, Issue 1 - Serial Number 19, May and June 2025, Pages 285-290 PDF (737.47 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.37652/juaps.2024.151635.1286 | ||
| Authors | ||
| Haytham Razooki Hassan* 1; Adraa Abbas Sadeq2 | ||
| 1Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq | ||
| 2Ministry of Education/General Directorate of Education in Maysan Governorate, Maysan, Iraq | ||
| Abstract | ||
| Let β± 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. γ∂_ γ_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) β± = πΌπ ( γd ' γ_(λ⁄μ )), where γd ' γ_(λ⁄μ)and γd ' γ_(λ⁄μ) :γβ±° γ_(λ⁄μ)β± βΆ _(γ ^Λγ_(λΜ ⁄ μΜ) ) 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. | ||
| Keywords | ||
| Weyl module; contracting; homotopy; divided power algebra | ||
| References | ||
|
[1] Akin K, David A B and Weyman J Schur Functors and Schur complexes Advances in mathematics 44,207_278 (1982).
[2] David A B and Rota, G C 2001 Approaches resolution of weyl modules Adv In Applied Math, 27 182-191.
[3] Hassan H R and Jasim N S 2018 On Free Resolution of Wely module and Zero Characteristic Resolution in the case of Partition (8,7,3), Baghdad Science Journal.
[4] Hassan H R and Abd -Alridah N SH 2020 Complex of Characteristic Zero in the Skew-Shape (8,6,3)/(u,1) where u=1 and 2,Iraqi Journal of Science, phys.: Conf.ser 1003(012051)1-15.
[5] L.R. Vermani , 2003 An elementry approach to homotopical algebra, Chapman and Hall /CRC, Monpgraphs and Surveys in pure and applied Mathematics 130. | ||
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