We show that all $2A$-Majorana representations of the Harada-Norton group $F_5$ have the same shape. If ${\mathcal R}$ 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 ${\mathcal R}$ is based on the (unique) embedding of $F_5$ in the Monster, $U$ is closed under the algebra product.
Franchi, C., Ivanov, A. A., Mainardis, M., The 2A-Majorana representations of the Harada-Norton group, <<ARS MATHEMATICA CONTEMPORANEA>>, 2016; 11 (1): 175-187. [doi:10.26493/1855-3974.859.0c3] [http://hdl.handle.net/10807/68917]
The 2A-Majorana representations of the Harada-Norton group
Franchi, Clara;
2016
Abstract
We show that all $2A$-Majorana representations of the Harada-Norton group $F_5$ have the same shape. If ${\mathcal R}$ 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 ${\mathcal R}$ is based on the (unique) embedding of $F_5$ in the Monster, $U$ is closed under the algebra product.
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