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Orbit Structure On The Silov Boundary Of A Tube Domain And The Plancherel Decomposition Of A Causally Compact Symmetric Space, With Emphasis On The Rank One Case, Troels Roussau Johansen

LSU Doctoral Dissertations

We construct a G-equivariant causal embedding of a compactly causal symmetric space G/H as an open dense subset of the Silov boundary S of the unbounded realization of a certain Hermitian symmetric space G₁/K₁ of tube type. Then S is an Euclidean space that is open and dense in the flag manifold G₁/P', where P' denotes a certain parabolic subgroup of G₁. The regular representation of G on L²(G/H) is thus realized on L²(S), and we use abelian harmonic analysis in the study thereof. In particular, …