In this paper we show that the symmetric group $S_n$ has a Majorana representation $(S_n, T, W, \phi, \psi)$ only if $n\leq 12$. The converse follows by a result of Simon Norton, who proved that the Monster group has a subgroup isomorphic to $S_{12}$. Further, we give the irreducible constituents and their dimensions of the ${\mathbb R}[S_n]$-modules generated by the axial vectors for $8\leq n\leq 12$
Standard Majorana Representations of the Symmetric Groups
MAINARDIS, Mario
2014-01-01
Abstract
In this paper we show that the symmetric group $S_n$ has a Majorana representation $(S_n, T, W, \phi, \psi)$ only if $n\leq 12$. The converse follows by a result of Simon Norton, who proved that the Monster group has a subgroup isomorphic to $S_{12}$. Further, we give the irreducible constituents and their dimensions of the ${\mathbb R}[S_n]$-modules generated by the axial vectors for $8\leq n\leq 12$File in questo prodotto:
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