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An Aspect of Icosahedral Symmetry

Published online by Cambridge University Press:  20 November 2018

Jan Rauschning  and
Peter Slodowy
Jan Rauschning
Affiliation:
Fachbereich Mathematik der Universität Hamburg Universität Hamburg D-20146 Hamburg Germany, e-mail: jan [email protected]
Peter Slodowy
Affiliation:
Fachbereich Mathematik der Universität Hamburg Universität Hamburg D-20146 Hamburg Germany, e-mail: [email protected]
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Abstract

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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.

Keywords

14L2420B25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 4 , 01 December 2002 , pp. 686 - 696
Copyright
Copyright © Canadian Mathematical Society 2002

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