On a class of generalized Gelfand pairs
Let G/H be a pseudo-Riemannian symmetric space of rank one. The author limits himself to the groups G which are the connected Lie subgroups of the simply connected complex Lie groups \(G_ c\) (the Lie algebra of \(G_ c\) is the complexification of the Lie algebra of G). The main result of the reviewed article is that all such pairs (G,H) are generalized Gelfand pairs (i.e. each continuous unitary representation of G which can be realized on G/H is multiplicity-free) except the pairs \((Spin(1,q+1)\), Spin(1,q)), \(q\geq 1\).
scientific article; zbMATH DE number 3992130