We show that all 2A-Majorana representations of the Harada-Norton group F5 have the same shape. If R is such a representation, we determine, using the theory of association schemes, the dimension and the irreducible constituents of the linear span U of the Majorana axes. Finally, we prove that, if R is based on the (unique) embedding of F5 in the Monster, U is closed under the algebra product.
@article{859,
title = {The 2A-Majorana representations of the Harada-Norton group},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {11},
year = {2015},
doi = {10.26493/1855-3974.859.0c3},
language = {EN},
url = {http://dml.mathdoc.fr/item/859}
}
Franchi, Clara; Ivanov, Alexander A.; Mainardis, Mario. The 2A-Majorana representations of the Harada-Norton group. ARS MATHEMATICA CONTEMPORANEA, Tome 11 (2015) . doi : 10.26493/1855-3974.859.0c3. http://gdmltest.u-ga.fr/item/859/