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Suppose      G = SL ( n , C ) G = {\text {SL}}(n,{\mathbf {C}})       or      SL ( n , R ) {\text {SL}}(n,{\mathbf {R}})       and      K K       is a maximal compact subgroup of      G G      . If      P P       is any parabolic subgroup of      G G      , we determine a system of differential equations on      G / K G/K       with the property that any function on      G / K G/K       satisfies these differential equations if and only if it is the Poisson integral of a hyperfunction on      G / P G/P      .

Generalized Hua-operators and parabolic subgroups. The cases of 𝑆𝐿(𝑛,𝐶) and 𝑆𝐿(𝑛,𝑅)