Supercategorified quantum groups beyond sl2

Prove that the supercategorified quantum groups constructed by Brundan and Ellis categorify the quantum covering group U_{q,π}(g) for all Cartan data g beyond sl2; specifically, establish that the decategorification of their super 2-Kac–Moody algebras is isomorphic to the corresponding quantum covering group U_{q,π}(g) in general type.

Background

Brundan and Ellis introduced supercategorified quantum groups (super 2-Kac–Moody algebras), building on earlier work by Kang, Kashiwara, Oh, and Tsuchioka. Their construction is conjectured to categorify Lusztig-type quantum covering groups U_{q,π}(g), which unify even and super cases via a parameter π.

The thesis notes that while this conjecture has been established for sl2, the general case for other Cartan data remains unresolved. Clarifying this would anchor odd/super knot homologies within a comprehensive higher representation-theoretic framework.