Source: Tohoku Math. J. (2) Volume 62, Number 2
(2010), 191-213.
We study relations between moment maps of Hamiltonian actions and isoparametric
hypersurfaces in spheres with four distinct principal curvatures. In this paper,
we deal with the isoparametric hypersurfaces given by the isotropy
representations of compact irreducible Hermitian symmetric spaces of classical
type and of rank two. We show that such isoparametric hypersurfaces can be
obtained by moment maps. More precisely, certain squared-norms of moment maps
coincide with Cartan-Münzner polynomials, which are
defining-equations, of above isoparametric hypersurfaces.
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