The quantum Frobenius morphism and its splitting are incompatible with the canonical basis for all finite-dimensional simple Lie algebras of rank ≥ threshold, with the obstruction occurring at the same elements as Leclerc's imaginary vectors and tight monomial cone failures.
Cones from quantum groups to tropical flag varieties
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Dual imaginary vectors, tight monomial cones and quantum Frobenius morphism
The quantum Frobenius morphism and its splitting are incompatible with the canonical basis for all finite-dimensional simple Lie algebras of rank ≥ threshold, with the obstruction occurring at the same elements as Leclerc's imaginary vectors and tight monomial cone failures.