Finite Multiplicities Beyond Spherical Spaces.

Let |$G$| be a real reductive algebraic group, and let |$H\subset G$| be an algebraic subgroup. It is known that 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. In this paper, we formulate and analyze a generalization of sphericity that implies finite multiplicities in |${\mathcal {S}}(G/H)$| for small enough irreducible representations of |$G$|⁠. [ABSTRACT FROM AUTHOR]