In this case there is a criterion due to Gelfand and Kazhdan for the pair (G,K) to satisfy GP2. Suppose that there exists an involutive anti-automorphism σ of G such that any (K,K)-double invariant distribution on G is σ-invariant. Then the pair (G,K) satisfies GP2. See.Israel Gelfand, David Kazhdan, Representations of the group GL(n,K) where K is a local field, Lie groups and their representations (Proc. Summer School, Bolyai János Math. Soc., Budapest, 1971), pp. 95--118. Halsted, New York (1975).A. Aizenbud, D. Gourevitch, E. Sayag : (GL_{n+1}(F),GL_n(F)) is a Gelfand pair for any local field F.
