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Let G be a connected simple linear Lie group and H in G a symmetric subgroupsuch that the corresponding symmetric space G/H is non-compactly causal. Weshow that any irreducible unitary representation of G leads naturally to a netof standard subspaces on G/H that is isotone, covariant and has theReeh--Schlieder and the Bisognano--Wichmann property. We also show that thisresult extends to the universal covering group of SL(2,R) which has someinteresting application to intersections of standard subspaces associated torepresentations of such groups. For this a detailed study of hyperfunction anddistribution vectors is needed. In particular we show that every H-finitehyperfunction vector is in fact a distribution vector.

Nets of standard subspaces on non-compactly causal symmetric spaces