Characteristic conditions for exotic parabolic phenomena

Determine the relationship between the occurrence of exotic parabolic-variety phenomena in small characteristics and numerical invariants of the semisimple group, such as its Coxeter number, and characterize the precise conditions under which these phenomena occur.

Background

The paper constructs a second family of examples over imperfect fields in which stabilizers of rational points contain no Borel subgroup. The construction uses special behavior in characteristic two and is associated with anisotropic quadratic spaces and very special isogenies.

The authors expect that these phenomena may be confined to small characteristics and may depend on numerical invariants of the group. They explicitly identify understanding this relationship and determining exact occurrence criteria as unresolved questions.