In the representation theory of a reductive algebraic group $G$ in positive characteristic $p$, there is a conjecture known as the Humphreys-Verma conjecture, which states that an indecomposable injective module for a Frobenius kernel $G_r$ of $G$ should lift uniquely to a module for $G$. There is also a refinement of the conjecture, known as Donkin's tilting conjecture, which specifies which $G$-module this lift should be (an indecomposable tilting module with a specified highest weight).

Both conjectures are known to be true when $p\geq 2h-2$ where $h$ is the Coxeter number, and while it is not particularly common to see statements formulated conditional on either conjecture, the condition $p\geq 2h-2$ is exceedingly common, and quite often this condition could be replaced by an assumption that one or both of the above conjectures are true.