Development from prehomogeneous vector spaces to weakly spherical homogeneous spaces

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The development of this year is a clarrification of weakly spherical homogeneous spaces obtained from dividing general linear groups by their irreducible algebraic inbgroups which we will call irreducible weakly spherical homogeneous spaces. The point is to clarify the relation between castling transforms and weakly sphericality. By doing this, we complete the clarrification corresponding to irreducible regular prehomogeneous spaces.