Fraser's upper generalized cluster algebra conjecture for quantum affine module categories

Let $cal C_{\varepsilon,xi}$ be the full subcategory of finite-dimensional modules of the restricted quantum loop algebra $U_\varepsilon^{{\rm res}}(Lmathfrak{sl}_k)$ determined by the bipartition $xi$, and let $K_0(cal C_{\varepsilon,xi})$ be its Grothendieck ring. Fraser's conjecture asserts that this ring admits an upper generalized cluster algebra structure in which every cluster monomial is the class of a simple module. The exchange degrees and initial quiver are those of the seed in Definition 7.2, with $N=(k-1)(ell-1)$, and the initial cluster has mutable variables identified with classes of the specified simple modules and frozen variables equal to $1$. This is a quantum-affine reformulation of Fraser's conjecture extending Gleitz's conjecture to arbitrary $k$ and $ell$; the asserted categorification and explicit initial seed remain conjectural.