Decomposition Matrix for the projective Characters S_28, p=11
DOI:
https://doi.org/10.31642/JoKMC/2018/110112%20Keywords:
Irreducible modular spin characters, Representation group, Decomposition matrix to the spin characters, projective character, 20c20, 20c30Abstract
In this work, we compute the decomposition matrix to the spin characteristics of S_28 for a given field of characteristic p=11, the connections between the irreducible modular spin characters and the irreducible spin characters of S_28. The technique employed in this study is (r,r ̅ )-inducing, which creates projective characters for S_28 by using the projective characters of S_27. Maple was used to seeing all available columns and then choosing the potentially appropriate columns of them. In order to explore irreducible modular spin characteristics, general correlations and theorems will be discovered as a result of this research.
Downloads
References
A. H. Jassim, “11-Brauer trees of S_20, “ Journal of Basrah Researches(Sciences).40, pp. 76-86, 2014.
A. H. Jassim, “11- Modular Characters for S ̅_27, ” Journal of University of Babylon for Pure and Applied Sciences. 27, pp. 303–317,2019.
A. H. Jassim, and M. M. Jawad, “Decomposition matrices for the spin characters of S_26 Modulo 11, ” Basrah Journal of Science. 37, pp. 253–261, 2019.
A. K. Yaseen, “Modular spin representations of the symmetric groups,” Ph.D. Dissertation, Aberystwyth University, Aberystwyth, Aberystwyth, United Kingdom, 1987.
A. O. Morris, "The spin representation of the symmetric group, ” proc. London Math, Soc., 3(12), pp.55-76, 1962
A. O. Morris, and A.K.Yaseen, “Decomposition matrices for spin characters of symmetric group,” Proc. of Royal society of Edinburgh. 108A,pp.145-164, 1988.
B. M. Puttaswamaiah, andJ. D. Dixon, “Modular representation of finite groups, ” New York, Academic Press, 1977.
G. James, “The modular characters of Mathieu groups, ” J. Algebra. 27, pp.57–111, 1973.
J. F. Humphreys, “Blocks of the Projective representations of symmetric groups, ” J. London Math. Society. 33, pp. 441-452, 1986.
J. F. Humphreys, “Projective modular representations of finite groups, ” J. London Math, Soc., 16, pp.51-66, 1977.
J. Schur, “Uber die Darstellung der symmetrischen und der alternierenden gruppe durch gebrochene lineare subtituttionen, ” j,Reine ang.Math. 139, pp.155-250, 1911.
N. M. Yacoob, “Decomposition Matrices of the Spin Characters of the Symmetric Group S_21, S_22 Modulo p=11 and S_22 modulo p=7, ” M.Sc. Thesis Basrah University. 2014.
S. A. Taban, and A. H. Jassim, “The Brauer trees of the symmetric groups S_17 and S_18 modulo p = 11, ” Basrah Journal of Science, 30A, pp. 149-165, 2012.
S. A. Taban, and A. H. Jassim, “Irreducible modular spin characters of the symmetric group S_19 modulo p = 11, ” Basrah Journal of Science 31A, pp. 59–74, 2013.
Downloads
Published
How to Cite
Issue
Section
Categories
License
Copyright (c) 2024 Ahmed Hussein Jassim, Saeed Taban
This work is licensed under a Creative Commons Attribution 4.0 International License.
which allows users to copy, create extracts, abstracts, and new works from the Article, alter and revise the Article, and make commercial use of the Article (including reuse and/or resale of the Article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made and the licensor is not represented as endorsing the use made of the work.
