Abstract
For G=SL(n,R) and K=SO(n) Akhiezer and Gindikin explicitly determine a G-invariant Stein extension ? of G/K in G C /K C . We give several other descriptions of ?. In terms of the geometry of an arbitrary flag variety for G C , ? is described as the “polar set” of the closed G-orbit. ? is also the space of “linear cycles” in an arbitrary open G-orbit. We also see that ? is a domain of holomorphy for Szego kernels associated to interesting irreducible representations of G.
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