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Symmetric homogeneous convex domains
Published online by Cambridge University Press: 22 January 2016
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Let D be a convex domain in the n-dimensional real number space Rn, not containing any affine line and A(D) the group of all affine transformations of Rn leaving D invariant. If the group A(D) acts transitively on D, then the domain D is said to be homogeneous. From a homogeneous convex domain D in Rn, a homogeneous convex cone V = V(D) in Rn+1 = Rn × R is constructed as follows (cf. Vinberg [11]):
which is called the cone fitted on the convex domain D.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1984
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