Finite multiplicities beyond spherical spaces (Q6623614)

Let \(G\) be a real reductive algebraic group, and let \(H \subset G\) be an algebraic subgroup. The action of \(G\) on the space of functions on \(G/H\) is ``tame'' if this space is spherical. In particular, the multiplicities of the space \(\mathcal{S}(G/H)\) of Schwartz functions on \(G/H\) are finite in this case. A. Aizenbud and D. Gourevitch formulate and analyze a generalization of sphericity that implies finite multiplicities in \(\mathcal{S}(G/H)\) for small enough irreducible representations of \(G\).