Outcome for the case (11,10; 1)
DOI:
https://doi.org/10.21123/bsj.2024.9905Keywords:
Divided power algebra, Letter place, Overlap, Place polarizations, Resolution, Weyl module.Abstract
Through this work R is a commutative ring with 1, is a free R-module and is the divided power algebra of degree . A partition of length ℓ(l) = n is a sequence = (l1, l2, …, ln) of non-negative integers in non-increasing order l1³ l2 ³ …³ ln > 0. The weight of a partition l is ÷l÷ = l1 + l2 + …+ ln. A relative sequence is a pair of sequences such that m £ l and denoted by . If both and are partitions then the relative sequence is called a skew partition. Let be the free generator of divided power algebra in one generator. The divided power element of degree of the free generator acts on by place polarization of degree from place 1 to place 2. The graded algebra acts on the graded module , the degree of the second factor determines the grading. M is a graded left odule, where for and , so we have: . This article surveys the exactness of the Weyl resolution of the sequence for the case (11,10; 1) after getting the contracting homotopy of { }; where = 0,1, …, 8, and the terms of the characteristic-free resolution for it.
Received 11/10/2023
Revised 04/03/2023
Accepted 06/03/2024
Published Online First 20/09/2024
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