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The 2A-Majorana representations of the Harada-Norton group. (English) Zbl 1394.20009
Summary: We show that all 2$$A$$-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.

MSC:
 20C34 Representations of sporadic groups 20D08 Simple groups: sporadic groups 05E30 Association schemes, strongly regular graphs 17B69 Vertex operators; vertex operator algebras and related structures
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