Extension of the fundamental-variable braid formula to arbitrary generalized Cartan matrices

Let $C$ be a generalized Cartan matrix, and let ${\overline{\mathcal{U}}}(\dot{{\mathbf f}t})$ denote the algebra whose fundamental variables are considered in Theorem. Arbitrary-type braid-formula conjecture. Theorem holds for arbitrary generalized Cartan matrices. The conjecture proposes that the braid group action computes the fundamental variables of ${\overline{\mathcal{U}}}(\dot{{\mathbf f}t})$ beyond the finite-type case; establishing this would extend the paper's braid-formula result to arbitrary types.