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An Aspect of Icosahedral Symmetry
Published online by Cambridge University Press: 20 November 2018
Abstract
We embed the moduli space $Q$ of 5 points on the projective line
${{S}_{5}}$-equivariantly into
$\mathbb{P}\left( V \right)$, where
$V$ is the 6-dimensional irreducible module of the symmetric group
${{S}_{5}}$. This module splits with respect to the icosahedral group
${{A}_{5}}$ into the two standard 3-dimensional representations. The resulting linear projections of
$Q$ relate the action of
${{A}_{5}}$ on
$Q$ to those on the regular icosahedron.
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- Research Article
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- Copyright © Canadian Mathematical Society 2002
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