spherical pair

Using this approach one can take any concepts of representation theory and generalize them to the case of spherical pair.

This conjecture is proven for a large class of spherical pairs including all the symmetric pairs.

In the context of algebraic groups the analogs of Gelfand pairs are called spherical pair.

It is conjectured that any spherical pair (G,K) over a local field satisfies the following weak version of the Gelfand property:

In this approach representation theory can be generalized by replacing the pair (G x G, G) by any spherical pair (G,K).