The dimension of the space of relatively invariant hyperfunctions on regular prehomogeneous vector spaces (Q1100247)

This paper deals with the estimate of the dimension of the space of relatively invariant hyperfunctions on a regular irreducible prehomogeneous vector space. Let \((G_{{\mathbb{C}}},\rho,V_{{\mathbb{C}}})\) be a regular irreducible prehomogeneous vector space and let \((G_{{\mathbb{R}}},\rho,V_{{\mathbb{R}}})\) be one of its real forms. The author conjectures that the space of relatively invariant hyperfunctions on \(V_{{\mathbb{R}}}\) coincides with the number of the connected components of \(V_{{\mathbb{R}}}-S_{{\mathbb{R}}}\) where \(S_{{\mathbb{R}}}\) is the real locus of the singular set of \((G_{{\mathbb{C}}},\rho,V_{{\mathbb{C}}})\). He proves that this conjecture is actually true in almost all the cases by case-by-case calculation.