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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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