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.
The 2A-Majorana representation of the Harada-Norton group
Franchi, Clara;Mainardis, Mario
2016-01-01
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.File in questo prodotto:
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