Tame irreducible super Yangian modules are thin

Let $\mathrm{Y}(\mathfrak{gl}_{m|n})$ be the super Yangian. A finite-dimensional irreducible module is tame and thin according to the weight-space conditions for $\mathrm{Y}(\mathfrak{gl}_{m|n})$-modules. Tameness–thinness conjecture. A finite-dimensional irreducible $\mathrm{Y}(\mathfrak{gl}_{m|n})$-module is tame only if it is thin. The analogous equivalence is known for the nonsuper Yangian and for quantum affine algebras of type B; the stated implication is proposed for the super Yangian.