Extension to other semisimple homogeneous spaces and twisted products

Extend rigidity for very non-generic elements to elements of Weyl chamber flows on other semisimple homogeneous spaces and on twisted products.

Background

The established theorem concerns very non-generic diagonal elements on compact quotients of SL_n(R). The authors observe that parts of the method extend to many R-split simple homogeneous spaces, but cases involving more general semisimple groups or non-R-split structures may require new mechanisms.

The unresolved problem is to determine whether the rigidity phenomenon persists for Weyl chamber-flow elements in these broader settings, including twisted products.