Open AccessModular Irreducible Representations of the FpW4-Submodules ,()pFNof the Modules ,()pFMas Linear Codes, where W4is the Weyl Group of Type B4
Author(s) -
Jinan F. N. Al-Jobory,
AUTHOR_ID,
Emad Bakr Al-Zangana,
Faez Hassan Ali,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2021
Publication title -
al-nahrain journal of science
Language(s) - English
Resource type - Journals
eISSN - 2663-5461
pISSN - 2663-5453
DOI - 10.22401/anjs.24.2.08
Subject(s) - mathematics , finite field , integer (computer science) , prime (order theory) , group (periodic table) , general linear group , type (biology) , linear subspace , modular group , field (mathematics) , order (exchange) , combinatorics , pure mathematics , discrete mathematics , algebra over a field , symmetric group , computer science , physics , ecology , quantum mechanics , biology , programming language , finance , economics
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 modules pFS ( , )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))()pU representing 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( , )()pUfor 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