The conjecture that every good symmetric pair is a GK pair

Let $(G,H)$ be a good symmetric pair, meaning a symmetric pair satisfying the goodness condition defined in the paper. A GK pair is a symmetric pair satisfying the Gelfand–Kazhdan distributional invariance criterion used there.

Good-pair GK conjecture. Every good symmetric pair is a GK pair.

The paper presents this as a generalization of the complex connected GK-pair conjecture. It is stated as a sufficient condition for the van Dijk conjecture, and no resolution is given in the supplied text.