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Generalized Hua-operators and parabolic subgroups. The cases of $ {\rm SL}(n,\,{\bf C})$ and $ {\rm SL}(n,\,{\bf R})$


Author: Kenneth D. Johnson
Journal: Trans. Amer. Math. Soc. 281 (1984), 417-429
MSC: Primary 22E46; Secondary 22E30, 43A85
MathSciNet review: 719678
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Abstract: Suppose $ G = {\text{SL}}(n,{\mathbf{C}})$ or $ {\text{SL}}(n,{\mathbf{R}})$ and $ K$ is a maximal compact subgroup of $ G$. If $ P$ is any parabolic subgroup of $ G$, we determine a system of differential equations on $ G/K$ with the property that any function on $ G/K$ satisfies these differential equations if and only if it is the Poisson integral of a hyperfunction on $ G/P$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0719678-3
Keywords: Hua-operators, parabolic subgroups, boundary
Article copyright: © Copyright 1984 American Mathematical Society