Geometric analysis of covariant maps in symmetric matrices reveals interesting properties involving conics.
The general problem of giving a geometric interpretation of a covariant map between rational representations is discussed.Geometric interpretations are then described for all irreducible prehomogeneous covariants of the prehomogeneous vector space mentioned in the title.The geometric interpretations lead naturally to interesting geometry involving pairs of conics in the projective plane.
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Kable Anthony C. (2014) studied this question.
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