TY - JOUR
ID -
TI - Modular Irreducible Representations of the FpW4-Submodules ,()pFNof the Modules ,()pFMas Linear Codes, where W4is the Weyl Group of Type B4
AU - Jinan F. N. Al-Jobory
AU - Emad B. Al-Zangana
AU - Faez Hassan Ali
PY - 2021
VL - 24
IS - 2
SP - 48
EP - 63
JO - Al-Nahrain Journal of Science مجلة علوم النهرين
SN - 26635453 26635461
AB -
The modular representations of the FpWn-Specht modules( , )KSas linear codes is given in our paper [6], and the modular irreducible representations of the FpW4-submodules( , )pFNof the Specht modulespFS ( , )as linear codes where W4is the Weyl group of type B4is given in our paper [5]. In this paper we are concerning of finding the linear codes of the representations of the irreducible FpW4-submodules( , )pFNof the FpW4-modules( , )pFMfor each pair of partitions( , )of a positive integer n4, where FpGF(p) is the Galois field (finite field) of order p, and pis a prime number greater than or equal to 3. We will find in this paper a generator matrix of a subspace((2,1),(1))()pUre presenting the irreducible FpW4-submodules((2,1),(1))pFNof the FpW4-modules((2,1),(1))pF Mand give the linear code of ((2,1),(1))()pU for each prime number p greater than or equal to 3. Then we will give the linear codes of all the subspaces( , )()pU for all pair of partitions( , )of a positive integer n4, and for each prime number p greater than or equal to 3.We mention that some of the ideas of this work in this paper have been influenced by that of Adalbert Kerber and Axel Kohnert [13], even though that their paper is about the symmetric group and this paper is about the Weyl groups of type Bn.
ER -